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

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300 cents Deborah Henry
Answer:

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

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Deborah Henry
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