Question 1019596
Given *[tex \large 3^{x+1} = 100], take the log base 3 of both sides to get


*[tex \large x+1 = \log_3 {100} \Rightarrow x = \log_3{100} - 1]


It's not immediate from the answer choices, but you can obtain the correct answer (which is actually A) by rewriting the value for x as *[tex \large \frac{\log_{10} {100}}{\log_{10} {3}} - 1] (using change-of-base). *[tex \large \log_{10} {100} = 2], so the expression is equivalent to


*[tex \large \frac{2}{\log_{10}{3}} - 1 = \frac{2 - \log_{10}{3}}{\log_{10}{3}], or choice A.