Solve for $x$ , $5^{l o g_{10} x} = 50 - x^{l o g_{10} 5}$

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Solution

$x^{l o g_{10} 5} = x^{l o g_{x} 5 l o g_{10} x} = 5^{l o g_{10} x}$
$∴ W e h a v e {2.5}^{l o g_{10} x} = 50 o r 5^{l o g_{10} x} = 5^{2}$
$∴ l o g_{10} x = 2 o r x = 10^{2} = 100$

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