Question

multiple choice 1 point 30) which of the following is the inverse of ( f(x) = 3(5^x) )? a. ( f^{-1}(x) = log_5 \frac{x}{3} ) b. ( f^{-1}(x) = \frac{log_5 x}{3} ) c. ( f^{-1}(x) = 3log_5 x ) d. ( f^{-1}(x) = log_{15} x ) a b c d

Explanation:

Step1: Set $y=f(x)$

$y = 3(5^x)$

Step2: Swap $x$ and $y$

$x = 3(5^y)$

Step3: Isolate the exponential term

$\frac{x}{3} = 5^y$

Step4: Convert to logarithmic form

$y = \log_{5}\frac{x}{3}$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = \log_{5}\frac{x}{3}$

Answer:

A. $f^{-1}(x)=\log_{5}\frac{x}{3}$