Question

do as directed (3) if 5^m+5-³=5⁵,then find m​

Answer 1

≻Given:-

• ${5}^{m} + {5}^{ - 3} = {5}^{5}$

≻To find:-

• m

≻Solution:-

$\implies5^m+5-³=5⁵ \\ \\ \\ \\ \\ \implies\frac{5 {}^{m} }{5 {}^{ - 3} } = {5}^{5} \\ \\ \\ \\ \\ \implies{5}^{m - ( - 3)} \\ \\ \\ \\ \\ \implies \therefore \: \bigg ( \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \bigg) \\ \\ \\ \\ \\ \implies{5}^{m + 3} = {5}^{5} \\ \\ \\ \\ \\ \implies m + 3 = 5 \\ \\ \\ \\ \\ \implies \: m = 5 - 3 \\ \\ \\ \\ \\ \implies \: \boxed{m = 2}$

Hence, The value of m = 2.