Question

If $(\frac{12}{13}{)}^4\times (\frac{13}{12}{)}^{-8}=(\frac{12}{13}{)}^{2x}$, then find the value of $x$.

Answer 1

$(\frac{12}{13}{)}^4\times (\frac{13}{12}{)}^{-8}=(\frac{12}{13}{)}^{2x}$

$⟹(\frac{12}{13}{)}^4\times (\frac{12}{13}{)}^8=(\frac{12}{13}{)}^{2x}$

$⟹(\frac{12}{13}{)}^{4+8}=(\frac{12}{13}{)}^{2x}$

$⟹(\frac{12}{13}{)}^{12}=(\frac{12}{13}{)}^{2x}$

$\therefore 2x=12⟹x=\frac{12}{2}=6$

Hence, $x=6$