Question

solve the equation.
$3^{x - 5} = 243$
$x = ?$

Explanation:

Step1: Express 243 as a power of 3

We know that \( 3^5 = 243 \), so we can rewrite the equation \( 3^{x - 5}=243 \) as \( 3^{x - 5}=3^5 \).

Step2: Set the exponents equal

Since the bases are the same (both are 3) and the exponential function is one - to - one, if \( a^m=a^n \) (where \( a>0,a
eq1 \)), then \( m = n \). So we have \( x - 5=5 \).

Step3: Solve for x

Add 5 to both sides of the equation \( x - 5 = 5 \). We get \( x=5 + 5=10 \).

Answer:

\( x = 10 \)