Question

Solve. Write your answer in simplest form using integers, fractions, and common logarithms.

2* = 7
X =

Answer 1

`\textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\\\ \textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2^x=7\implies \log(2^x)=\log(7)\implies x\log(2)=\log(7) \\\\\\ x=\cfrac{\log(7)}{\log(2)}\implies x=\log_2(7)`