Question

1. solve: $5^{x} = 5^{3x - 10}$

Explanation:

Step1: Use exponential equality property

If \( a^m = a^n \) (where \( a>0, a
eq1 \)), then \( m = n \). Here \( a = 5 \), \( m = x \), \( n = 3x - 10 \), so \( x=3x - 10 \).

Step2: Solve linear equation

Subtract \( x \) from both sides: \( 0 = 2x - 10 \). Add 10 to both sides: \( 2x = 10 \). Divide by 2: \( x = 5 \).

Answer:

\( x = 5 \)