What is log_{10}(f)-1/3 log_{10}(g)+4log_{10}(h) ?

The solution to log_{10}(f)-1/3 log_{10}(g)+4log_{10}(h) is log_{10}((fh^4g^{2/3})/g)

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simplify log_{10}(f)-1/3 log_{10}(g)+4log_{10}(h)

simplify

lo g_{10} (f) - \frac{1}{3} lo g_{10} (g) + 4 lo g_{10} (h)

lo g_{10} (\frac{f h ^{4} g ^{\frac{2}{3}}}{g})

Solution steps

lo g_{10} (f) - \frac{1}{3} lo g_{10} (g) + 4 lo g_{10} (h)

Apply log rule:

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

\frac{1}{3} lo g_{10} (g) = lo g_{10} (g^{\frac{1}{3}})

= lo g_{10} (f) - lo g_{10} (g^{\frac{1}{3}}) + 4 lo g_{10} (h)

Apply log rule:

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

lo g_{10} (f) - lo g_{10} (g^{\frac{1}{3}}) = lo g_{10} (\frac{f}{g ^{\frac{1}{3}}})

= lo g_{10} (\frac{f}{g ^{\frac{1}{3}}}) + 4 lo g_{10} (h)

Simplify

\frac{f}{g ^{\frac{1}{3}}} : \frac{f g ^{\frac{2}{3}}}{g}

= lo g_{10} (\frac{f g ^{\frac{2}{3}}}{g}) + 4 lo g_{10} (h)

Apply log rule:

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

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

= lo g_{10} (\frac{f g ^{\frac{2}{3}}}{g}) + lo g_{10} (h^{4})

Apply log rule:

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

lo g_{10} (\frac{f g ^{\frac{2}{3}}}{g}) + lo g_{10} (h^{4}) = lo g_{10} (\frac{f g ^{\frac{2}{3}}}{g} h^{4})

= lo g_{10} (\frac{f g ^{\frac{2}{3}}}{g} h^{4})

Simplify

\frac{f g ^{\frac{2}{3}}}{g} h^{4} : \frac{f h ^{4} g ^{\frac{2}{3}}}{g}

= lo g_{10} (\frac{f h ^{4} g ^{\frac{2}{3}}}{g})

ln (\frac{10 - 0.319}{22.4 - 0.319})

ln (x) + ln (- \frac{y}{x} + 1)

lo g_{a} (\frac{x ^{4}}{y ^{2} a ^{4}})

2 lo g_{10} (x) - 2 lo g_{10} (x + 1)

ln (- 2 e^{- x})

What is log_{10}(f)-1/3 log_{10}(g)+4log_{10}(h) ?
The solution to log_{10}(f)-1/3 log_{10}(g)+4log_{10}(h) is log_{10}((fh^4g^{2/3})/g)