What is log_{10}(x)-1/2 log_{10}(y)+4log_{10}(z) ?

The solution to log_{10}(x)-1/2 log_{10}(y)+4log_{10}(z) is log_{10}((xz^4sqrt(y))/y)

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simplify log_{10}(x)-1/2 log_{10}(y)+4log_{10}(z)

simplify

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 4 lo g_{10} (z)

lo g_{10} (\frac{x z ^{4} y}{y})

Solution steps

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 4 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}}) + 4 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}}}) + 4 lo g_{10} (z)

Simplify

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

= lo g_{10} (\frac{x y}{y}) + 4 lo g_{10} (z)

Apply log rule:

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

4 lo g_{10} (z) = lo g_{10} (z^{4})

= lo g_{10} (\frac{x y}{y}) + lo g_{10} (z^{4})

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^{4}) = lo g_{10} (\frac{x y}{y} z^{4})

= lo g_{10} (\frac{x y}{y} z^{4})

Simplify

\frac{x y}{y} z^{4} : \frac{x z ^{4} y}{y}

= lo g_{10} (\frac{x z ^{4} y}{y})

tanh (\frac{1}{2} lo g_{10} (\frac{1 + z}{1 - z}))

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

lo g_{10} (\frac{27 a}{b})

ln (\frac{x}{x - 4}) + ln (\frac{x + 4}{x}) - ln (x^{2} - 16)

3 lo g_{10} (x) + lo g_{10} (2)

What is log_{10}(x)-1/2 log_{10}(y)+4log_{10}(z) ?
The solution to log_{10}(x)-1/2 log_{10}(y)+4log_{10}(z) is log_{10}((xz^4sqrt(y))/y)