We need to solve the equation $95000 = 10000(1.05)^{4x}$ for $x$ and round the answer to three decimal places.

1. Problem Description

We need to solve the equation $95000 = 10000(1.05)^{4x}$ for $x$ and round the answer to three decimal places.

2. Solution Steps

First, divide both sides of the equation by 10000:

$\frac{95000}{10000} = \frac{10000(1.05)^{4x}}{10000}$

$9.5 = (1.05)^{4x}$

Next, take the natural logarithm of both sides:

$\ln(9.5) = \ln((1.05)^{4x})$

Use the power rule of logarithms, $\ln(a^b) = b\ln(a)$:

$\ln(9.5) = 4x \ln(1.05)$

Now, solve for $x$ by dividing both sides by $4\ln(1.05)$:

$x = \frac{\ln(9.5)}{4\ln(1.05)}$

Using a calculator, we have

$\ln(9.5) \approx 2.25129$

$\ln(1.05) \approx 0.04879$

$x \approx \frac{2.25129}{4(0.04879)} \approx \frac{2.25129}{0.19516} \approx 11.5355$

Rounding to three decimal places, we get $x \approx 11.536$.

3. Final Answer

$x = \frac{\ln(9.5)}{4\ln(1.05)} \approx 11.536$