The solution for the equation. Use the change of base formula to approximate axact answer to the nearest hundredth when approximate. $2\times {10}^{x}=66$ .

zi2lalZ
2021-09-13
Answered

The solution for the equation. Use the change of base formula to approximate axact answer to the nearest hundredth when approximate. $2\times {10}^{x}=66$ .

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doplovif

Answered 2021-09-14
Author has **71** answers

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:

$2\times {10}^{x}=66$

$10}^{x}=\frac{66}{2$

${10}^{x}=33$

$x={\mathrm{log}}_{10}\left(33\right)$

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$x\approx 1.52$ .

Change of base formula for logarithm is given by

Calculation:

Change to an logarithmic equation

Conclusion:

The solution for the given equation is

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