Question

multiple choice 1 point

1. which is the inverse of $y = \log_5(x + 1)$?

a. $y = \log_{x + 1}5$
b. $y = 5^{x - 1}$
c. $y = 5^{x + 1}$
d. $y = 5^x - 1$
a b c d

Explanation:

Step1: Rewrite log to exponential form

Given $y = \log_{5}(x+1)$, convert to exponential form:
$$5^y = x + 1$$

Step2: Solve for x

Isolate x by subtracting 1 from both sides:
$$x = 5^y - 1$$

Step3: Swap x and y for inverse

Replace x with y and y with x to get the inverse function:
$$y = 5^x - 1$$

Answer:

D. $y = 5^x - 1$