Answer the following questions based on integral exponents.

MATHEMATICS · Multi-part · CBSE · Mathematics · Power Play · Power Play

Problem

Answer the following questions based on integral exponents. (i) Prove that if

a \neq 0

and

a^{m}=a^{n}

for integers

m

and

n

, then

m=n

. (ii) Using the result of part (i), solve

3^{4x-7}=3^{2x+9}

for

x

. (iii) Verify your value of

x

by substituting it back into the given equation.