Question

Solve 4^(x+2) = 12 for x using the change of base formula log base b of y equals log y over log b

Answer 1

`\bf \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} \\\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf 4^(x+2)=12\implies \stackrel{\textit{exponential form}}{\log_4(12)=x+2}\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_(10)(12)}{\log_(10)(4)}} = x + 2 \\\\\\ \cfrac{\log_(10)(12)}{\log_(10)(4)} - 2 = x\implies -0.2075 \approx x`