Question

If 8 to the power m+3 upon 2 to the power 2 = 2 to the power 4m, then what is the value of m?

Answer 1

Given :-

${\dfrac{8^{m\: +\: 3}}{2^{2}}}\: =\: 2^{4m}$

To Find :-

The value of m

Solution :-

We know that,

if we equalise the base on both L.H.S and R.H.S then the powers also gets equalised.

Now,

${\dfrac{8^{m\: +\: 3}}{2^{2}}}\: =\: 2^{4m}$

$\implies\:{8^{m\: +\: 3}}\: =\: 2^{4m}\: \times\: 2^{2}$

since, the bases are same on RHS therefore we can use the formula :-

$m^{x}\:\times\: m^{y}\: =\: m^{x + y}$

$\implies\: 8^{m\: +\: 3}\: =\: 2^{4m + 2}$

Now,

$\implies\: 2^{3(m\: +\: 3)}\: =\: 2^{4m + 2}$

$\implies\: 2^{3m\: +\: 9}\: =\: 2^{4m + 2}$

Since the bases are equal on both sides therefore, powers will also be equal

=> 3m + 9 = 4m + 2

=> 3m - 4m = 2 - 9

=> -m = -7

=> m = 7

Therefore, m = 7

Answer 2

Correct answer:

m = 7.

⊱ ──────  ✯  ────── ⊰

$\to \sf \dfrac{8^{m+3}}{2^2} = 2^{4m}$

$\to \sf 8^{m+3} = 2^{4m} \times 2^2$

$\boxed{\sf{\blue{Use:a^b \times a^c = a^{b+c}}}}$

$\to \sf 8^{m+3} = 2^{4m+2}$

$\boxed{\sf{\blue{Write \ 8 \ as \ 2^3 }}}$

$\to \sf 2^{3(m+3)} = 2^{4m+2}$

$\to \sf 2^{3m+9} = 2^{4m+2}$

$\boxed{\sf{\blue{Equate \ the \ bases}}}$

$\to \sf 3m+9 = 4m+2$

$\to \sf 3m-4m = 2-9$

$\sf \to -m = -7$

$\leadsto \sf{\purple{m = 7}}$

$\red \therefore \Large \frak{\green{Value \ of \ m = 7}}$