What is 7log_{10}(x)-1/2 log_{10}(y) ?

The solution to 7log_{10}(x)-1/2 log_{10}(y) is log_{10}((x^7sqrt(y))/y)

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simplify 7log_{10}(x)-1/2 log_{10}(y)

simplify

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

lo g_{10} (\frac{x ^{7} y}{y})

Solution steps

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

Apply log rule:

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

7 lo g_{10} (x) = lo g_{10} (x^{7})

= lo g_{10} (x^{7}) - \frac{1}{2} lo g_{10} (y)

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^{7}) - lo g_{10} (y^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} (x^{7}) - lo g_{10} (y^{\frac{1}{2}}) = lo g_{10} (\frac{x ^{7}}{y ^{\frac{1}{2}}})

= lo g_{10} (\frac{x ^{7}}{y ^{\frac{1}{2}}})

Simplify

\frac{x ^{7}}{y ^{\frac{1}{2}}} : \frac{x ^{7} y}{y}

= lo g_{10} (\frac{x ^{7} y}{y})

lo g_{10} (2) - \frac{1}{2 ln ( 10 )}

6 ln (6) - 4 ln (4) - 2

ln (\frac{0.1}{0.9})

\frac{1}{2 a} (ln \frac{u}{a} + 1 - ln \frac{u}{a} - 1) + C

ln (x (y + 1))

What is 7log_{10}(x)-1/2 log_{10}(y) ?
The solution to 7log_{10}(x)-1/2 log_{10}(y) is log_{10}((x^7sqrt(y))/y)