Question

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. $y = 5^{x} - 1$

Explanation:

Step1: Rewrite log as exponential

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

Step2: Solve for x

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

Step3: Swap x and y for inverse

Replace $x$ with $y$ and $y$ with $x$:
$y = 5^x - 1$

Answer:

D. $y = 5^x - 1$