Question

The value of x satisfying the equation $4^{{{\log }_9}^3}+9^{{{\log }_2}^4}={10}^{{{\log }_c}^{83}}$ is

Answer 1

$4^{{\log }_9^3}+9^{{\log }_2^4}={10}^{{\log }_c^{83}}$

$\Rightarrow (4{)}^{1/2\left({\log }_{3}3\right)}+(9{)}^{2{\log }_{2}2}={10}^{{\log }_c\left(83\right)}$

$\Rightarrow (4{)}^{1/2}+(9{)}^2={10}^{{\log }_c\left(83\right)}$

$\Rightarrow 2+81={10}^{{\log }_c\left(83\right)}$

$\Rightarrow 83={10}^{{\log }_c\left(83\right)}$

$\Rightarrow {\log }_{10}\left(83\right)={\log }_c\left(83\right)$

$\Rightarrow c=10$