Answer would be 24 hope this is right
A true
because 53•(41•11)=23,903 and (53•41)•11=23,903
Hope this helped
Take the logarithm of both sides. The base of the logarithm doesn't matter.
![4^{5x} = 3^{x-2}](https://tex.z-dn.net/?f=4%5E%7B5x%7D%20%3D%203%5E%7Bx-2%7D)
![\implies \log 4^{5x} = \log 3^{x-2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Clog%204%5E%7B5x%7D%20%3D%20%5Clog%203%5E%7Bx-2%7D)
Drop the exponents:
![\implies 5x \log 4 = (x-2) \log 3](https://tex.z-dn.net/?f=%5Cimplies%205x%20%5Clog%204%20%3D%20%28x-2%29%20%5Clog%203)
Expand the right side:
![\implies 5x \log 4 = x \log 3 - 2 \log 3](https://tex.z-dn.net/?f=%5Cimplies%205x%20%5Clog%204%20%3D%20x%20%5Clog%203%20-%202%20%5Clog%203)
Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :
![\implies 5x \log 4 - x \log 3 = - 2 \log 3](https://tex.z-dn.net/?f=%5Cimplies%205x%20%5Clog%204%20-%20x%20%5Clog%203%20%3D%20-%202%20%5Clog%203)
![\implies x (5 \log 4 - \log 3) = - 2 \log 3](https://tex.z-dn.net/?f=%5Cimplies%20x%20%285%20%5Clog%204%20-%20%5Clog%203%29%20%3D%20-%202%20%5Clog%203)
Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :
![\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7Bx%20%3D%20-%5Cdfrac%7B%202%20%5Clog%203%20%7D%7B%205%20%5Clog%204%20-%20%5Clog%203%20%7D%7D)
You can stop there, or continue simplifying the solution by using properties of logarithms:
![\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }](https://tex.z-dn.net/?f=%5Cimplies%20x%20%3D%20-%5Cdfrac%7B%20%5Clog%203%5E2%20%7D%7B%20%5Clog%204%5E5%20-%20%5Clog%203%20%7D)
![\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }](https://tex.z-dn.net/?f=%5Cimplies%20x%20%3D%20-%5Cdfrac%7B%20%5Clog%209%20%7D%7B%20%5Clog%201024%20-%20%5Clog%203%20%7D)
![\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7Bx%20%3D%20-%5Cdfrac%7B%20%5Clog%209%20%7D%7B%20%5Clog%20%5Cfrac%7B1024%7D3%20%7D%7D)
You can condense the solution further using the change-of-base identity,
![\implies \boxed{x = -\log_{\frac{1024}3}9}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7Bx%20%3D%20-%5Clog_%7B%5Cfrac%7B1024%7D3%7D9%7D)
Answer:
-6.25 tI am not sure if this can help you but this is what I got