Question

find the value of m for which 3^m/3^-5=3^8​

Answer 1

Question:

Find the value of m for the given equation, $\frac{3^m}{3^{-5}} = 3^8$

Answer:

$\fbox{\bold{\red{\mathsf{m = 3}}}}$

Step-by-step explanation:

$\frac{3^m}{3^{-5}} = 3^8$

$3^{m - (-5)} = 3^8\:(\because \frac{a^m}{a^n} = a^{m-n}; m>n)$

$3^{m + 5} = 3^8\:[\because (-) \times (-) = +]$

m + 5 = 8 (as base is same).

m = 8 - 5

$\fbox{\mathsf{\bold{\pink{m = 3}}}}$

So, the value of m is 3.

But the value that we've gotta is correct or not? Let's check.

By substituting the value of m by 3. So,

$\frac{3^m}{3^{-5}} = 3^8$ will be,

$\frac{3^3}{3^{-5}} = 3^8$

$3^{3 - (-5)} = 3^8\:(\because \frac{a^m}{a^n} = a^{m-n}; m>n)$

$3^{3+5} = 3^8$

3⁸ = 3⁸

$\fbox{\bold{\mathsf{\purple{L.H.S = R.H.S}}}}$

So, the value of m is 3.