What is 3log_{3}(x)-7log_{3}(y) ?

The solution to 3log_{3}(x)-7log_{3}(y) is log_{3}((x^3)/(y^7))

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simplify 3log_{3}(x)-7log_{3}(y)

simplify

3 lo g_{3} (x) - 7 lo g_{3} (y)

lo g_{3} (\frac{x ^{3}}{y ^{7}})

Solution steps

3 lo g_{3} (x) - 7 lo g_{3} (y)

Apply log rule:

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

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

= lo g_{3} (x^{3}) - 7 lo g_{3} (y)

Apply log rule:

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

7 lo g_{3} (y) = lo g_{3} (y^{7})

= lo g_{3} (x^{3}) - lo g_{3} (y^{7})

Apply log rule:

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

lo g_{3} (x^{3}) - lo g_{3} (y^{7}) = lo g_{3} (\frac{x ^{3}}{y ^{7}})

= lo g_{3} (\frac{x ^{3}}{y ^{7}})

1.75 ln ∣ y + 2 ∣ + 0.25 ln ∣ y - 3 ∣ + 2 ln ∣ y ∣

4 - \frac{1}{2} ln (2) - 1 + \frac{1}{2} ln (\frac{1}{2})

lo g_{8} (\frac{( x - 4 ) ( x - 1 ) ( 3 )}{5 x})

ln (k y) - ln (k x)

ln (24) - 8 ln (2)

What is 3log_{3}(x)-7log_{3}(y) ?
The solution to 3log_{3}(x)-7log_{3}(y) is log_{3}((x^3)/(y^7))