Question

Which of the following is the value of 'm' in 6m/ 6-3 = 65?
I. -3
II. -2
III. 3
IV. 2

Answer 1

The question given to us is:

$\frac{6^m}{6^{-3}}=6^5$

This can be re-written as:

$6^{m-(-3)}=6^5$ ($\since \frac{a^m}{a^n}=a^{m-n}$)

Thus, we get:

$6^{m+3}=6^5$

Now, comparing the exponents in the above equation, we will get:

$m+3=5$

$\therefore m=5-3=2$

Thus, the last option, option IV, m=2, is the correct option.

Answer 2

Answer:

6m+3=65

m+3=5

m=5-3=2