Question

If 36 Superscript 12 minus m Baseline = 6 Superscript 2 m, what is the value of m?

Answer 1

Answer:

For given equation the value m=6

That is the value of m is 6.

Step-by-step explanation:

Given equation can be written as

$36^{12-m}=6^{2m}$

Now to find the value of m in the equation:

$36^{12-m}=6^{2m}$

$36^{12}.36^{-m}=6^{2m}$  ( using $a^{m+n}=a^m.a^n$) Here m=12 and n=-m

$36^{12}.36^{-m}=(6^{2})^{m}$ (using $(a^m)^{n}=a^{mn}$) Here m=2 and n=m

$\frac{36^{12}}{36^{m}}=(6^{2})^{m}$  (using the property $a^{m-n}=\frac{a^m}{a^n}$ Here m=12 and n=m

$\frac{36^{12}}{36^{m}}=36^{m}$

Now multiplying $36^{m}$ on both sides

$\frac{36^{12}}{36^{m}}\times 36^{m}=36^{m}\times 36^{m}$

$36^{12}=36^{m+m}$  ( using $a^{m+n}=a^m.a^n$) Here m=m and n=m

$36^{12}=36^{2m}$

In the above we have base numbers are same so that we can equate  the powers of these numbers

12=2m

Rewritting the equation

$2m=12$

$m=\frac{12}{2}$

m=6

Therefore the value of m is 6.

For given equation the value m=6.

Answer 2

Answer:

B.6

Step-by-step explanation: