Question

Solve each exponential equation. Give the exact value for x. 5^x=8

Answer 1

`\textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\[-0.35em] ~\dotfill\\\\ 5^x=8\implies \log(5^x)=\log(8)\implies x\log(5)=\log(8) \\\\\\ x=\cfrac{\log(8)}{\log(5)}\implies x\approx 1.29`