Question

Solve for the variable in the equations below. Round your answers to the nearest hundredth. Do not round any intermediate computations. E^x=11 4^-9y=7

Answer 1

`\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array}~\hfill~ \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \underset{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^(log_a (x))=x \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}`

`e^x=11\implies \log_e(e^x)=\log_e(11)\implies x=\log_e(11) \\\\\\ x=\ln(11)\implies x\approx 2.40 \\\\[-0.35em] ~\dotfill\\\\ 4^(-9y)=7\implies \log(4^(-9y))=\log(7)\implies -9y\log(4)=\log(7) \\\\\\ -9y=\cfrac{\log(7)}{\log(4)}\implies y=\cfrac{\log(7)}{-9\log(4)}\implies y\approx -0.16`