Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\log^{5x}=-8$$

Answer

$$x=1/10^1.5157165665104$$

Solution


Take the \(5\)th root of both sides.
\[\log{x}=\sqrt[5]{-8}\]
Simplify exponent.
\[\log{x}=-1.515717\]
Use Definition of Common Logarithm: \({b}^{a}=x\) if and only if \(log_b(x)=a\).
\[x={10}^{-1.515717}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[x=\frac{1}{{10}^{1.515717}}\]

Decimal Form: 0.030499

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