What is the answer to solvefor y,log_{10}(xy)=y ?

The answer to solvefor y,log_{10}(xy)=y is y=-(\W(-(ln(10))/x))/(ln(10))

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solvefor y,log_{10}(xy)=y

solve for

y, lo g_{10} (x y) = y

y = - \frac{W ( - \frac{l n ( 10 )}{x} )}{ln ( 10 )}

Solution steps

lo g_{10} (x y) = y

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

1 0^{l o g_{10} (x y)} = 1 0^{y}

Simplify

1 0^{l o g_{10} (x y)} : y x

y x = 1 0^{y}

Solve

y x = 1 0^{y} : y = - \frac{W ( - \frac{l n ( 10 )}{x} )}{ln ( 10 )}

y = - \frac{W ( - \frac{l n ( 10 )}{x} )}{ln ( 10 )}

Verify Solutions:

y = - \frac{W ( - \frac{l n ( 10 )}{x} )}{ln ( 10 )}

True

The solution is

y = - \frac{W ( - \frac{l n ( 10 )}{x} )}{ln ( 10 )}

x = ln (x + 1)

\frac{x}{4} = lo g_{2} (x)

x, 0.3 = - lo g_{10} (x)

ln (4 x - 3) = ln (9) - ln (x - 3)

lo g_{3} (x + 1) = lo g_{3} (x - 1)

What is the answer to solvefor y,log_{10}(xy)=y ?
The answer to solvefor y,log_{10}(xy)=y is y=-(\W(-(ln(10))/x))/(ln(10))