Question

pre - calculus cp ic 25 - 26 solving equations using properties of logarithms. which statement is true for log_3 (x + 1)=2? 2(x + 1)=3; x + 1 = 3^2; x + 1 = 2^3; 3(x + 1)=2

Explanation:

Step1: Recall log - exponent conversion

If $\log_{a}b = c$, then $b=a^{c}$. Given $\log_{3}(x + 1)=2$, by the definition of logarithms, we can rewrite it in exponential form.
Since $\log_{3}(x + 1)=2$, we have $x + 1=3^{2}$.

Step2: Calculate the value of $3^{2}$

$3^{2}=9$, so $x + 1 = 9$.

Answer:

None of the provided options are correct. If we solve $\log_{3}(x + 1)=2$ correctly, we get $x+1 = 3^{2}=9$. If we assume there was a mis - typing in the options and we consider the correct concept of converting from logarithmic to exponential form, the correct exponential form of $\log_{3}(x + 1)=2$ is $x + 1=3^{2}$.