Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth. \[ 0.04 \cdot(1.19)^{x}=4 \]

Step 1 ：The given equation is in the form of a * b^x = c. To solve for x, we can first divide both sides by 0.04 to isolate the exponential term. This gives us \((1.19)^{x} = 100.0\).

Step 2 ：Next, we can take the natural logarithm (ln) of both sides to bring down the exponent. This gives us \(x \cdot ln(1.19) = ln(100.0)\), or equivalently, \(x \cdot 0.17395330712343798 = 4.605170185988092\).

Step 3 ：Finally, we can solve for x by dividing both sides by ln(1.19). This gives us \(x = \frac{4.605170185988092}{0.17395330712343798}\), which simplifies to \(x = 26.474\).

Step 4 ：Final Answer: The solution to the equation \(0.04 \cdot(1.19)^{x}=4\) is \(x = \boxed{26.474}\).