Question

\(\left(\dfrac{3}{4}\right)^x\) = \(\dfrac{2^8}{3^4}\)

( x - 2 )⁸ = 3 ( x - 2 )⁶

Answer 1

❏\(\left(\dfrac{3}{4}\right)^x=\dfrac{4^4}{3^4}\)

\(\Rightarrow\left(\dfrac{3}{4}\right)^x=\left(\dfrac{4}{3}\right)^4\)

\(\Rightarrow\left(\dfrac{3}{4}\right)^x=\dfrac{1}{\left(\dfrac{3}{4}\right)^4}\)

\(\Rightarrow x=-4\)

Answer 2

❏\(\left(x-2\right)^8=3\left(x-2\right)^6\)

\(\Rightarrow\left(x-2\right)^2=3\)

\(\Rightarrow x-2=\sqrt{3}\)

\(\Rightarrow x=\sqrt{3}+2\)