Question

solve the equation $2^x = 8$. if no solution exists, enter none.

Explanation:

Step1: Express 8 as a power of 2

We know that \( 8 = 2^3 \), so the equation \( 2^x = 8 \) can be rewritten as \( 2^x = 2^3 \).

Step2: Use the property of exponents

For exponential functions with the same base (\( a^m = a^n \) implies \( m = n \) when \( a > 0, a
eq 1 \)), since the base here is 2 (which is greater than 0 and not equal to 1), we can set the exponents equal to each other. So \( x = 3 \).

Answer:

\( x = 3 \)