Question

ONLY THE BRAINLIEST CAN ANSWER THIS:
FIND THE VALUE OF x WHICH SATISFIES THE FOLLOWING EQUATION:
$log_{10}( \frac{ {x}^{ \frac{1}{x} } }{ {x}^{ \frac{1}{x + 1} } } ) = \frac{1}{5050}$
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Answer 1

Answer:

tried it many times and it went bit of lengthy , i reached until

log10(x1/(x2+x))

then i multiplied 2 both numerator and denominator and then it is consecutive terms in denominator I got my answer 100. Just want to know if it is correct and a shorter way to solve it ?

Step-by-step explanation:

This is equivalent to

log(x1x(1+x))=15050

Then:

x1x(1+x)=102100∗101

Or

x1x(1+x)=1001100∗101

Thus x=100.