Question

Solve for X:
(i) $6^x=\frac{1}{216}$
(ii) $2^x=4^{2x+1}$

Answer 1

(i) $6^x=\frac{1}{216}$

$\Rightarrow 6^x=\frac{1}{6^3}$

$\Rightarrow 6^x=6^{-3}$

Equating the exponents we get $x=-3$

(ii)$2^x=4^{2x+1}$

$\Rightarrow 2^x=(2^2{)}^{2x+1}$

$\Rightarrow 2^x=2^{2(2x+1)}$

$\Rightarrow 2^x=2^{4x+2}$

Equating the exponents we get

$x=4x+2$

$\Rightarrow 3x=-2$

$\Rightarrow x=-\frac{2}{3}$