Question

Solve : x^(log_(2)a)+a^(log_(2)x)=2a^(2) where a>1​

Answer 1

Step-by-step explanation:

We have,

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

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

$\implies2 {a}^{ log_{2}(x) } = 2 {a}^{2}$

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

$\implies log_{2}(x) = 2$

$\implies \: x = 4$