If b^n = b^m, then what values of m and n satisfies the equation, (for b ≠ 0)?
- m = 0 and n = 0
- n = 1 and m = 0
- n = 0 and m = 1
- None of these
Explanation
Given b^n = b^m, for b ≠ 0:
Step 1: Analyze the equation
If b^n = b^m, then n = m, or b = 1 or b = -1 with specific conditions on n and m.
Step 2: Consider the case when b ≠ 1 and b ≠ -1
For b ≠ 0, 1, or -1, the equation holds true when n = m.
Step 3: Look for an option that satisfies n = m
Among the given options, one possible solution where n = m is when both n and m are 0, since any non-zero number to the power of 0 is 1.
The answer is: m = 0 and n = 0.
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