To solve the logarithmic equation \(\log(8x^3) = 4\), you can use the properties of logarithms. Here's how you can do it:
1. Apply the definition of logarithms to rewrite the equation:
\(8x^3 = 10^4\)
2. Now, simplify the right side of the equation by evaluating \(10^4\):
\(8x^3 = 10000\)
3. Divide both sides by 8 to isolate \(x^3\):
\(x^3 = \frac{10000}{8}\)
4. Calculate the right side:
\(x^3 = 1250\)
5. To find \(x\), take the cube root of both sides:
\(x = \sqrt[3]{1250}\)
\(x \approx 10.079\)
So, the solution to the equation is approximately \(x \approx 10.079\).