Question

For the following, find all the real numbers x that satisfy the equation. If none satisfy the equation then state the answer as "None". $( \frac{25}{4} )}^ { - 3x} = \frac{3125}{32}$(25/4)^-3x = 3125/32

Answer 1

Solution

For this case we have the following:

$(\frac{25}{4})^{-3x}=\frac{3125}{32}$

We can apply natural log in both sides and we have:

$-3x\ln (\frac{25}{4})=\ln (\frac{3125}{32})$

And then we can solve for x like this:

$x=-\frac{1}{3}\cdot\frac{\ln (\frac{3125}{32})}{\ln (\frac{25}{4})}=-\frac{5}{6}$

Then the solution for this case is :

x= -5/6