What is log_{10}(x)-1/2 log_{10}(y)+6log_{10}(z) ?

The solution to log_{10}(x)-1/2 log_{10}(y)+6log_{10}(z) is log_{10}((xz^6sqrt(y))/y)

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simplify log_{10}(x)-1/2 log_{10}(y)+6log_{10}(z)

simplify

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 6 lo g_{10} (z)

lo g_{10} (\frac{x z ^{6} y}{y})

Solution steps

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 6 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{10} (y) = lo g_{10} (y^{\frac{1}{2}})

= lo g_{10} (x) - lo g_{10} (y^{\frac{1}{2}}) + 6 lo g_{10} (z)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x) - lo g_{10} (y^{\frac{1}{2}}) = lo g_{10} (\frac{x}{y ^{\frac{1}{2}}})

= lo g_{10} (\frac{x}{y ^{\frac{1}{2}}}) + 6 lo g_{10} (z)

Simplify

\frac{x}{y ^{\frac{1}{2}}} : \frac{x y}{y}

= lo g_{10} (\frac{x y}{y}) + 6 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 lo g_{10} (z) = lo g_{10} (z^{6})

= lo g_{10} (\frac{x y}{y}) + lo g_{10} (z^{6})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (\frac{x y}{y}) + lo g_{10} (z^{6}) = lo g_{10} (\frac{x y}{y} z^{6})

= lo g_{10} (\frac{x y}{y} z^{6})

Simplify

\frac{x y}{y} z^{6} : \frac{x z ^{6} y}{y}

= lo g_{10} (\frac{x z ^{6} y}{y})

- lo g_{10} (1.75 \cdot 1 0^{- 5})

lo g_{2} (\frac{4 x + 1}{x})

2 lo g_{4} (x) - lo g_{4} (y) - \frac{1}{2} lo g_{4} (z)

lo g_{5} (\frac{3 x + 2}{x + 1})

ln (\frac{e ^{x l n (2)}}{2})

What is log_{10}(x)-1/2 log_{10}(y)+6log_{10}(z) ?
The solution to log_{10}(x)-1/2 log_{10}(y)+6log_{10}(z) is log_{10}((xz^6sqrt(y))/y)