Take the logarithm of both sides. The base of the logarithm doesn't matter.
[tex]4^{5x} = 3^{x-2}[/tex]
[tex]\implies \log 4^{5x} = \log 3^{x-2}[/tex]
Drop the exponents:
[tex]\implies 5x \log 4 = (x-2) \log 3[/tex]
Expand the right side:
[tex]\implies 5x \log 4 = x \log 3 - 2 \log 3[/tex]
Move the terms containing x to the left side and factor out x :
[tex]\implies 5x \log 4 - x \log 3 = - 2 \log 3[/tex]
[tex]\implies x (5 \log 4 - \log 3) = - 2 \log 3[/tex]
Solve for x by dividing boths ides by 5 log(4) - log(3) :
[tex]\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}[/tex]
You can stop there, or continue simplifying the solution by using properties of logarithms:
[tex]\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }[/tex]
[tex]\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }[/tex]
[tex]\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}[/tex]
You can condense the solution further using the change-of-base identity,
[tex]\implies \boxed{x = -\log_{\frac{1024}3}9}[/tex]
Which model represents the equation 4w+3=3w+6
Answer:
w=3 (please give me brianliestt!!)
Step-by-step explanation:
4w+3=3w+6 (subtract 3 from both sides)
-3 -3
4w=3w+3 (subtract 3w on both sides)
-3w -3w
1w=3 (divide by 1)
w=3
PLEASE HELP URGENT!!!!
Answer:
The answer is the second option.
Step-by-step explanation:
Because if you add all of the x you get 11 and you have 4+4 left over so the answer is 11x+8. Hope this helps!
please help me with this question....
Answer:
Person D
Step-by-step explanation: Because when you subtract the deductions from what the people earned. Person D has the least amount of money.
(PLEASE HELP ASAP)
Graph: y < 1/3x + 1/2
Find the values of X
Answer:
x=8
Step-by-step explanation:
1. 91+12x-7=180 2. 68=7x+12
84+12x=180 56=7x
12x=96 8=x
x=8
Consecutive angles Alternate Interior Angles
whats 9999999999+××888899182764urydujdh7w73747
Answer:
.0589582125/*6.059852 cuhhhhh
Step-by-step explanation:
What is 18.5 percent of 369
Answer:
68.265% is your answer
Step-by-step explanation:
Happy Holidays!!
((3 + 5)2.7) - 11 - 42
Answer:
-31.4
Step-by-step explanation:
[tex]2.7(3+5)-11-42\\=2.7*8-11-42\\=21.6-53\\=-31.4[/tex]
please help. online school hasn’t taught me anything and i’m failing math
Answer:
the picture is black
Step-by-step explanation:
Solve the following system of equations using matrices:
4x + 5y = 40
X-y=1
I need help solving question number 9!
Answer:
yes; [0, infinity); (0, -3)
During a sale a shirt was marked down from $70 to $56 what was the percent decrease
Answer:
-20%
Step-by-step explanation:
At Imelda's fruit stand, you bought 5 apples and 4 oranges for $10 dollar sign, 10, and your friend bought 5 apples and 5 oranges for $11dollar sign, 11.
Using this information, is it possible to determine the cost of one apple and one orange from the fruit stand? If so, what do they cost? If not, why not?
Answer:
Step-by-step explanation:
we have
5apples+4 oranges=10
5apples+5oranges=11
from here we can say
5a=10-4 oranges
replace in the second equation
10-4 oranges+5oranges=11
1 orange=1 dollar
that means that 5apples =6 dollars
1apple=1.20 dollars
which line appears to have an x-intercept of -5 and a y-intercept of 3?
Answer:
Are there supposed to be a picture?
Step-by-step explanation:
Answer:
Graph G
Step-by-step explanation:
Graph G
Calculate the area of the shaded region. Show ALL of your work
Answer:
100
Step-by-step explanation:
The area of the non-shaded spot is 8x10, which is 80.
The area of the entire rectangle is (8+4)x(10+5) = 180.
So, to find just the shaded region, subtract the nonshaded region (80) from the entire reactangle (180) to get 100
I need help on this question
Answer:
d
Step-by-step explanation:
Charles ran 30 ft in 4 seconds At this rate, how many yards can Charles run in 3 minutes?
After working for 24h Zoe made 234$ after working 40h zoe made 390$ predict how much she will make after 10h of work
Answer:
She will make $97.5 after 10 hours of work
Step-by-step explanation:
What is the perimeter of this figure?
6x+6
6x+10
4x+6
4x+8
Answer: 4x+8
Step-by-step explanation:
Okay since the area for the block is X, two numbers multiplied together is X.
Since the big block has an area of X^2, then this shows the sides to be X.
This gives the sides of the block with area X to be 1 and X.
Now just add up every side like this : 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + x + x + x + x to get 4x+8
PLZ HELP FAST (20 points I think)
Answer:
a greater slop is your answer your welcome
Answer:
a greater slope. The y-interpret will be 110t
Step-by-step explanation:
A team of five kids is randomly chosen from a class of 20 students. An outcome of the selection process is the set of five kids selected. What is the size of the same space
Answer:
[tex]S= 4[/tex]
Step-by-step explanation:
Given
[tex]Total = 20[/tex]
[tex]Selection = 5[/tex]
Required
Determine the size of sample space
Represent this with S
S is calculated by dividing the total number of kids by the number of selection.
[tex]S = \frac{Total}{Selection}[/tex]
[tex]S = \frac{20}{5}[/tex]
[tex]S= 4[/tex]
Hence, the sample space has a size of 4
I WILL GIVE 20 POINTS PLUS IM GIVING BRAINLIEST!!!!!!!
Answer:
I'm thinking B
Step-by-step explanation:
but I'm not 100
What is the probability of flipping a coin 10 times and getting heads 3 times?
Round answer to the nearest tenth of a percent
Answer:
8.1%
Step-by-step explanation:
A P E X
Please help me Asp with this
Answer:
13/24 more
Step-by-step explanation:
Dina = 5/6
Natasha = 11/8
Find the LCF
6| 6, 12, 18, 24
8| 8, 16, 24
Get each fraction to have a denominator of 24
5/6 = 20/24
11/8 = 33/24
Subtract 20/24 from 33/24
33/24 - 20/24 = 13/24
What is the answer to this equation, 8/x=5/9?
Answer:
The answer is 14.4.
Step-by-step explanation:
Cross multiply.
8*9 = 72
5*x = 5x
72 = 5x
^ Divide both sides by 5
72/5 = 14.4
14.4 = x
Answer:
14.4
Step-by-step explanation:
8/x = 5/9 Cross Multiply
5*x = 8 * 9 Combine the right
5x = 72 Divide by 5
5x/5 = 72/5
x = 14.4
Alfonso runs 10 km at an average speed of x km/h.
The next day he runs 12 km at an average speed of (x - 1) km/h.
The time taken for the 10km run is 30 minutes less than the time taken for the 12 km run.
(a) (i)
Write down an equation in x and show that it simplifies to x? – 5x – 20 = 0.
Step-by-step explanation:
Note that t = d/r where t is time, d is distance, and r is rate/speed.
We can come up with two equations with the information given and the equation:
t_1 hr = (10 km)/(x km/hr)
t_2 hr = (12 km)/(x - 1 km/hr)
where t_1 is the time taken to run the 10km the first day and t_2 is the time taken to run the 12km the second day.
We know that 30 minutes is 1/2 of an hour and that t_1 is 30 minutes less than t_2 (as stated in the question). Therefore, we can write:
t_1 = t_2 - 1/2
Substituting the values we derived:
(10 km)/(x km/hr) = (12 km)/(x - 1 km/hr) -1/2
Then we can evaluate by multiplying by 2x(x-1) on both sides:
20(x-1) = 24x - (x)(x-1)
20x - 20 = 24x - x^2 + x
x^2 -5x -20 = 0
And we are done.
I hope this helps! :)
An equation is formed when two equal expressions. The equation for the time can be written as (12/x-1)-(10/x)=0.5. The value of x is 7.623.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A.) Given Alfonso runs 10 km at an average speed of x km/h. Therefore, the time taken by Alfonso to rum 10km is 10/x hour.
Also, The next day he runs 12 km at an average speed of (x - 1) km/h. Therefore, the time taken by Alsonso to run 12km is 12/(x-1) hour.
Now, the time taken for the 10km run in 30minutes(0.5 hours) is less than the time taken for the 12 km run. Therefore, we can write,
[tex]\dfrac{12}{(x-1)}-\dfrac{10}{x} =0.5[/tex]
The equation for the time can be written as (12/x-1)-(10/x)=0.5.
B.) The value of x can be written as,
[tex]\dfrac{12}{(x-1)}-\dfrac{10}{x} =0.5\\\\12x-10(x-1)=0.5 \times x \times (x-1)\\\\12x - 10x +10 = 0.5x^2-0.5x\\\\2x+10 = 0.5x^2-0.5x\\\\0=0.5x^2 - 2.5x -10\\\\x = -2.623, 7.623[/tex]
Since the time can not be negative. Hence, the value of x is 7.623.
Learn more about Equation:
https://brainly.com/question/2263981
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10x-5 9x+2 is my equation and I don’t know how to solve it I really need help,someone please help me solve it.
9514 1404 393
Answer:
x = 7
Step-by-step explanation:
You solve a linear equation by putting the variable on one side of the equal sign and a constant on the other side. Here, variables and constants are on both sides of the equal sign, so you need to separate them.
The basic idea is that you add the opposite of any term you don't want. Whenever you perform any operation (like "add"), you must do it to both sides of the equation.
We observe that x-terms have coefficients of 10 and 9. We choose to add the opposite of 9x to both sides:
10 -9x -5 = 9x -9x +2
x -5 = 2 . . . . simplify
Now, we still have -5 on the left, where we don't want it. So, we add its opposite (+5) to both sides:
x -5 +5 = 2 +5
x = 7 . . . . simplify
The solution is x = 7.
_____
Additional comment
If we were to end up with an x-coefficient other than 1, we would divide both sides of the equation by that coefficient. This will leave the x-term with a coefficient of 1.
3(x + 8) – 4x < 2x + 9
Complete each of the 2 activities for this Task.
Activity 1 of 2
Solve the inequality for x. Show your work!
Explain how you would graph your solution on a number line. (type of circle, direction of arrow...)
Answer:
x > 5
Step-by-step explanation:
3x + 24 - 4x < 2x + 9
-x + 24 < 2x + 9
15 < 3x
3x > 15
x > 5
on a number line you would circle the 5 (don't shade in) and draw an arrow pointing to the right
Find the percent increase or decrease for each of the following values (Indicate whether each is an increase or a decrease). y to 0.78y
Answer:
y to 0.78y is a decrease
Step-by-step explanation:
y by itself can also be written as 1y, and 0.78y is less than 1, thus y to 0.78y is a decrease.
can u guys pretty please help
