What is log_{10}(1/x y^{((1-x))/x}) ?

The solution to log_{10}(1/x y^{((1-x))/x}) is ((1-x)log_{10}(y))/x-log_{10}(x)

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simplify log_{10}(1/x y^{((1-x))/x})

simplify

lo g_{10} (\frac{1}{x} y^{\frac{( 1 - x )}{x}})

\frac{( 1 - x ) lo g _{10} ( y )}{x} - lo g_{10} (x)

Solution steps

lo g_{10} (\frac{1}{x} y^{\frac{1 - x}{x}})

Simplify

\frac{1}{x} y^{\frac{1 - x}{x}} : \frac{y ^{\frac{1 - x}{x}}}{x}

= lo g_{10} (\frac{y ^{\frac{1 - x}{x}}}{x})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{y ^{\frac{1 - x}{x}}}{x}) = lo g_{10} (y^{\frac{1 - x}{x}}) - lo g_{10} (x)

= lo g_{10} (y^{\frac{1 - x}{x}}) - lo g_{10} (x)

Simplify

lo g_{10} (y^{\frac{1 - x}{x}}) : \frac{( 1 - x ) lo g _{10} ( y )}{x}

= \frac{( 1 - x ) lo g _{10} ( y )}{x} - lo g_{10} (x)

ln (\frac{1}{2 π} e^{- \frac{( y - θ ) ^{2}}{2}})

ln (\frac{e ^{3}}{6})

2 lo g_{5} (x) - lo g_{5} (x^{3})

\frac{1}{2} ln (\frac{25}{9})

- lo g_{10} (1.854 \cdot 1 0^{- 4})

What is log_{10}(1/x y^{((1-x))/x}) ?
The solution to log_{10}(1/x y^{((1-x))/x}) is ((1-x)log_{10}(y))/x-log_{10}(x)