Question

Find the value of n when :
i) $5^{2n}\times 5^3=5^9$
ii) $8\times 2^{n+2}=32$

Answer 1

(1)

$5^{2n}\times 5^3=5^9$

Apply law of exponents $x^a\times x^b=x^{a+b}$

$5^{2n+3}=5^9$

$\Rightarrow 2n+3=9$

$2n=9-3$

$2n=6$

$n=3$

(2)

$8\times 2^{n+2}=32$

$2^3\times 2^{n+2}=2^5$

Apply law of exponents $x^a\times x^b=x^{a+b}$

$2^{3+n+2}=2^5$

$2^{n+5}=2^5$

$\Rightarrow n+5=5$

$n=5-5$

$n=0$