Question

Given the exponential function f(x)=2^x. Explain how to convert this equation to a logarithmic function when f(x)=8 to solve for x.

Answer 1

x=3

Explanation:

Exponential Equations

The exponential function is the inverse of the logarithmic function. To solve exponential equations, we can use the logarithmic properties to isolate the variable.

The equation to solve is

`2^x=8`

Since x is an exponent, it's not possible to isolate it directly. We should take logarithms on both sides of the equation:

`log(2^x)=log8`

We haven't specified the base of the logarithm because it's not important for this equation to be solved. However, let's assume base-10 logs.

Rewriting the equation, we have

`log(2^x)=log(2^3)`

Applying the power rule of logarithms

`xlog2=3log2`

Simplifying by log2

`\boxed{x=3}`