What is log_{10}(a) 1/4-log_{10}(b) 1/2 ?

The solution to log_{10}(a) 1/4-log_{10}(b) 1/2 is log_{10}((a^{1/4}sqrt(b))/b)

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simplify log_{10}(a) 1/4-log_{10}(b) 1/2

simplify

lo g_{10} (a) \frac{1}{4} - lo g_{10} (b) \frac{1}{2}

lo g_{10} (\frac{a ^{\frac{1}{4}} b}{b})

Solution steps

lo g_{10} (a) \frac{1}{4} - lo g_{10} (b) \frac{1}{2}

Apply log rule:

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

\frac{1}{4} lo g_{10} (a) = lo g_{10} (a^{\frac{1}{4}})

= lo g_{10} (a^{\frac{1}{4}}) - \frac{1}{2} lo g_{10} (b)

Apply log rule:

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

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

= lo g_{10} (a^{\frac{1}{4}}) - lo g_{10} (b^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} (a^{\frac{1}{4}}) - lo g_{10} (b^{\frac{1}{2}}) = lo g_{10} (\frac{a ^{\frac{1}{4}}}{b ^{\frac{1}{2}}})

= lo g_{10} (\frac{a ^{\frac{1}{4}}}{b ^{\frac{1}{2}}})

Simplify

\frac{a ^{\frac{1}{4}}}{b ^{\frac{1}{2}}} : \frac{a ^{\frac{1}{4}} b}{b}

= lo g_{10} (\frac{a ^{\frac{1}{4}} b}{b})

4 lo g_{10} (x) - 6 lo g_{10} (x + 2)

lo g_{10} (\frac{10 z}{9})

ln (\frac{x ^{2} y ^{3}}{z ^{5}})

lo g_{5} (60) - lo g_{5} (50) + lo g_{5} (30)

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

What is log_{10}(a) 1/4-log_{10}(b) 1/2 ?
The solution to log_{10}(a) 1/4-log_{10}(b) 1/2 is log_{10}((a^{1/4}sqrt(b))/b)