Question

If 36^12 - m = 6^2m, what is the value of m?
a) 4
b) 6
c) 8
d) 9

Answer 1

To solve the equation 36^12 - m = 6^2m for the value of m, we can equate the exponents and simplify. The value of m is 12.

Step-by-step explanation:

To solve the equation 36^12 - m = 6^2m for the value of m, we need to equate the exponents. First, we raise 36 to the power of 12 and 6 to the power of 2:

1. 36^12 = (6^2)^12 = 6^24
2. Therefore, we have 6^24 - m = 6^2m
3. Next, we can rewrite 6^2m as (6^2)^m = 36^m
4. Now we have the equation 6^24 - m = 36^m
5. Since the bases are the same, we can equate the exponents: 24 - m = m
6. Combining like terms, we get 24 = 2m
7. Dividing both sides by 2, we get m = 12
8. Therefore, the value of m is 12.