Solve for x in: 3^(x-m)=5^(x-m)

Answer 1

To solve the equation \(3^{(x - m)} = 5^{(x - m)}\), we can start by rewriting it as:

\[ \left(\frac{3}{5}\right)^{(x - m)} = 1 \]

This equality holds true if the exponent \((x - m)\) is zero, since any number raised to the power of 0 is equal to 1. Thus, we can set the exponent equal to zero:

\[ x - m = 0 \]

Solving for \(x\) gives:

\[ x = m \]

Thus, the solution is:

\[ \boxed{m} \]