# The solution for the equation. Use the change of base formula to approximate axa

The solution for the equation. Use the change of base formula to approximate axact answer to the nearest hundredth when approximate. $2×{10}^{x}=66$.
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Formula used:
Change of base formula for logarithm is given by ${\mathrm{log}}_{a}x=\frac{{\mathrm{log}}_{b}x}{{\mathrm{log}}_{b}a}$, for $a>0$ and $x>0$
Calculation:
$2×{10}^{x}=66$
${10}^{x}=\frac{66}{2}$
${10}^{x}=33$
$x={\mathrm{log}}_{10}\left(33\right)$
Change to an logarithmic equation
$x=\frac{\mathrm{log}\left(33\right)}{\mathrm{log}\left(10\right)}$ Using the Change of Base Formula
$x=\frac{1.5185}{1}\mathrm{log}\left(13\right)=1.5185$ and $\mathrm{log}\left(10\right)=1$
$x\approx 1.52$
Conclusion:
The solution for the given equation is $x\approx 1.52$.