Question

What is the exact value of x in the exponential equation 2^5x − 57 = 43?

Answer 1

Start by getting the term with the exponent on one side
$2^{5x}=100$

take the log of both sides
$log 2^{5x} =log100$

There is a log rule that says we can bring down the exponent
$5xlog2=log100$

Solve for x
$5x= \frac{log100}{log2}$
5x=6.64

answer: x=1.33