What is 1/3 log_{10}(x)-2log_{10}(y) ?

The solution to 1/3 log_{10}(x)-2log_{10}(y) is log_{10}((x^{1/3})/(y^2))

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simplify 1/3 log_{10}(x)-2log_{10}(y)

simplify

\frac{1}{3} lo g_{10} (x) - 2 lo g_{10} (y)

lo g_{10} (\frac{x ^{\frac{1}{3}}}{y ^{2}})

Solution steps

\frac{1}{3} lo g_{10} (x) - 2 lo g_{10} (y)

Apply log rule:

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

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

= lo g_{10} (x^{\frac{1}{3}}) - 2 lo g_{10} (y)

Apply log rule:

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

2 lo g_{10} (y) = lo g_{10} (y^{2})

= lo g_{10} (x^{\frac{1}{3}}) - lo g_{10} (y^{2})

Apply log rule:

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

lo g_{10} (x^{\frac{1}{3}}) - lo g_{10} (y^{2}) = lo g_{10} (\frac{x ^{\frac{1}{3}}}{y ^{2}})

= lo g_{10} (\frac{x ^{\frac{1}{3}}}{y ^{2}})

- \frac{3}{10} lo g_{2} (\frac{3}{10}) - \frac{7}{10} lo g_{2} (\frac{7}{10})

ln (x^{10} 7 - x)

ln (10) + 6 ln (x) + 3 ln (x^{2} + 2)

ln (\frac{( 0 - 1 )}{0.5})

ln (3) + ln (5)

What is 1/3 log_{10}(x)-2log_{10}(y) ?
The solution to 1/3 log_{10}(x)-2log_{10}(y) is log_{10}((x^{1/3})/(y^2))