Solve the following equation:
$5^{log x} = 50 - x^{log 5}$

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Solution

$5^{log x} = 50 - x^{log 5} \Rightarrow 5^{log x} = 50 - 5^{log x} \Rightarrow {2.5}^{log x} = 50 \Rightarrow 5^{log x} = 25 \Rightarrow log x = 2$

Therefore, $x = 100.$

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x^{log 5} = 50

I f x = 10 \times 3^{k}

{log}_{3} x {log}_{4} x {log}_{5} x = {log}_{3} x {log}_{4} x + {log}_{4} x {log}_{5} x + {log}_{5} x {log}_{3} x

5^{log x} + 5^{log 5} = 3 (a > 0)

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