Find value of n if $7^{2n} = 49 \times 7^n$.

Given :

The given expression is $7^{2n} = 49 \times 7^n$.

To do :

We have to find the value of n.

Solution :

We know that,

$a^m + a^n = a^{m+n}$

$7^{2n} = 49 \times 7^n$

$7^{2n} = 7^2 \times 7^n$

$7^{2n} = 7^{2+n}$

Comparing the powers on both sides,

$2n = 2+n$

$2n-n = 2$

$n = 2$.

The value of n is 2.

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Updated on: 10-Oct-2022

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