Given that 7 m -7 n- then m - n isA- None of theseB- always greater than zeroC- always less than zeroD- can be equal to zero

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Given that 7 ...

Question

Given that $7^{m} > 7^{n}$ , then m-n is

always greater than zero

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always less than zero

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can be equal to zero

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None of these

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Solution

The correct option is A
always greater than zero

There are many cases here:
Case 1: If m and n are positive
So, m-n will be greater than zero
Case 2: if m is positive and n is negative
So, m-n will be positive
Case 3: if m is negative and n is negative. So, for $7^{m} > 7^{n}$ , the value of m should be greater than n

So, m-n will be positive.

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Given that 7m>7n, then m-n is

Given that $7^{m} > 7^{n}$ , then m-n is