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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Simplify

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

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

ln (\frac{sin ( x )}{cos ( x )})

4 lo g_{6} (x) - 3 lo g_{6} (y)

3 ln (x) - (ln (x + 1) + ln (x))

lo g_{7} (\frac{n}{2})

lo g_{10} (28) + 3 lo g_{10} (8 (42)) - 2.92

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