We are asked to solve the equation $95000 = 10000(1.05)^{4x}$ for $x$ and give the answer correct to 3 decimal places.

1. Problem Description

We are asked to solve the equation $95000 = 10000(1.05)^{4x}$ for $x$ and give the answer correct to 3 decimal places.

2. Solution Steps

We start with the given equation:

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

First, divide both sides by 10000:

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

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

Next, take the natural logarithm (ln) of both sides:

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

Using the property of logarithms, $\ln(a^b) = b\ln(a)$, we have:

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

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 to find the values of the logarithms:

$\ln(9.5) \approx 2.25129$

$\ln(1.05) \approx 0.04879$

Substitute these values into the equation for $x$:

$x = \frac{2.25129}{4(0.04879)}$

$x = \frac{2.25129}{0.19516}$

$x \approx 11.5355$

Rounding to 3 decimal places, we have:

$x \approx 11.536$

3. Final Answer

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