Question

solving for an exponent
logarithmic functions can be used to solve an equation for a variable that is in an exponent. if you take the log of both sides o identities to solve for the variable
part b
if $75^x = 21$, what is the value of $x$
express your answer with three digits to the right of the decimal point.
view available hint(s)
$x = $

Explanation:

Step1: Take log of both sides

$\log(75^x) = \log(21)$

Step2: Apply log power rule

$x\log(75) = \log(21)$

Step3: Isolate x

$x = \frac{\log(21)}{\log(75)}$

Step4: Calculate decimal value

$x \approx \frac{1.3222}{1.8751} \approx 0.705$

Answer:

0.705