Question

Solve the logarithmic equation ​

Answer 1

The solution to the logarithmic equation
`\(\log_x(512) = 3\)` is x = 8.

To solve the logarithmic equation
`\(\log_x(512) = 3\)`, we can rewrite it in exponential form. The logarithmic equation is essentially saying "the logarithm base x of 512 is equal to 3." So, in exponential form:

`\[ x^3 = 512 \]`

Now, we want to find the values of x that satisfy this equation. In this case, x is the cube root of 512:

`\[ x = \sqrt[3]{512} = 8 \]`

So, x = 8 is the solution to the logarithmic equation
`\(\log_x(512) = 3\)`.