Question

solve the equation $3^x = 81$. if no solution exists, enter none.
$x = $

Explanation:

Step1: Express 81 as a power of 3

We know that \( 81 = 3^4 \), so the equation \( 3^x = 81 \) can be rewritten as \( 3^x = 3^4 \).

Step2: Use the property of exponential functions

If \( a^m = a^n \) (where \( a>0,a
eq1 \)), then \( m = n \). Here, \( a = 3 \), \( m = x \), and \( n = 4 \). So we can conclude that \( x = 4 \).

Answer:

\( x = 4 \)