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

2. Solution Steps

First, divide both sides of the equation by $10000$:

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

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

Next, take the natural logarithm of both sides:

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

Using the logarithm power rule, we can rewrite the right side:

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

Now, isolate $x$ by dividing both sides by $4 \cdot ln(1.05)$:

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

Calculate the value:

$x = \frac{2.251298}{4 \cdot 0.048790}$

$x = \frac{2.251298}{0.19516}$

$x \approx 11.5357$

Rounding to 3 decimal places:

$x \approx 11.536$

3. Final Answer

1

1. 536