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Question

**Solve each equation. Give answers .correct to three decimal places**

$25,000=10,000(1.05)^{2 x}$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 2$\begin{aligned} 25000&=10000\left(1,05\right)^{2x}\\ \\ \dfrac{25000}{10000}&=1,05^{2x}\\ \\ 2,5&=1,05^{2x}\\ \\ \log2,5&=\log1,05^{2x}\\ \\ \log2,5&=2x\log1,05\\ \\ 2x&=\dfrac{\log2,5}{\log1,05}\\ \\ x&=\dfrac{\dfrac{\log2,5}{\log1,05}}{2}\\ \\ &\boxed{x=9,390} \end{aligned}$

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