Remove parentheses.
\[{20}^{-x}=7\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{1}{{20}^{x}}=7\]
Multiply both sides by \({20}^{x}\).
\[1=7\times {20}^{x}\]
Divide both sides by \(7\).
\[\frac{1}{7}={20}^{x}\]
Use Definition of Common Logarithm: \({b}^{a}=x\) if and only if \(log_b(x)=a\).
\[\log_{20}{\frac{1}{7}}=x\]
Use Change of Base Rule: \(\log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}\).
\[\frac{\log{\frac{1}{7}}}{\log{20}}=x\]
Switch sides.
\[x=\frac{\log{\frac{1}{7}}}{\log{20}}\]
Decimal Form: -0.649561
x=log(1/7)/log(20)
