Question

Find the value of $n$ in the following $7^{2n+1}÷49=7^3$

Answer 1

The giving term is

$7^{2n+1}÷49=7^3$

$\Rightarrow 7^{2n+1}÷7^2=7^3$ $\therefore 7^2=49$

$\Rightarrow 7^{2n+1}=7^3\times 7^2$

$\Rightarrow 7^{2n+1}=7^5$ [using formula $a^n+a^m=a^{\left(m+n\right)}$]

$\Rightarrow 2n+1=5$ [base are same so it cancel both side]

$\Rightarrow 2n=5-1$

$\Rightarrow 2n=4$

$\Rightarrow n=\frac{4}{2}$

$\therefore n=2$

Hence $n=2$