Question

solve x to the power log a by 2 + a to the power log x by 2 equal to 2 a square please solve fast​

Answer 1

Answer:

$\huge \pink{x = 4}$

Since

${a}^{ log_{b}(c) } = {c}^{ log_{b}(a) } \\so \\ {x}^{ log_{2}(a) } = {a}^{ log_{2}(x) }$

${x}^{ log_{2}(a) } + {a}^{ log_{2}(x) } = 2 {a}^{2} \\ \implies \\{a}^{ log_{2}(x) } + {a}^{ log_{2}(x) } = 2 {a}^{2} \\ 2a {}^{log_{2}(x) } = 2 {a}^{2} \\ {a}^{ log_{2}(x) } = {a}^{2} \\ log_{2}(x) = 2 \\ x = {2}^{2} = 4$