What is 3log_{10}(x)-6log_{10}(y) ?

The solution to 3log_{10}(x)-6log_{10}(y) is log_{10}((x^3)/(y^6))

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simplify 3log_{10}(x)-6log_{10}(y)

simplify

3 lo g_{10} (x) - 6 lo g_{10} (y)

lo g_{10} (\frac{x ^{3}}{y ^{6}})

Solution steps

3 lo g_{10} (x) - 6 lo g_{10} (y)

Apply log rule:

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

3 lo g_{10} (x) = lo g_{10} (x^{3})

= lo g_{10} (x^{3}) - 6 lo g_{10} (y)

Apply log rule:

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

6 lo g_{10} (y) = lo g_{10} (y^{6})

= lo g_{10} (x^{3}) - lo g_{10} (y^{6})

Apply log rule:

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

lo g_{10} (x^{3}) - lo g_{10} (y^{6}) = lo g_{10} (\frac{x ^{3}}{y ^{6}})

= lo g_{10} (\frac{x ^{3}}{y ^{6}})

ln (11) + 6 ln (x) + 6 ln (y)

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

lo g_{10} (\frac{4 x}{5})

lo g_{3} (5) + lo g_{3} (10)

ln (\frac{e ^{9}}{5})

What is 3log_{10}(x)-6log_{10}(y) ?
The solution to 3log_{10}(x)-6log_{10}(y) is log_{10}((x^3)/(y^6))