What is 5log_{3}(x)+3log_{3}(y) ?

The solution to 5log_{3}(x)+3log_{3}(y) is log_{3}(x^5y^3)

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simplify 5log_{3}(x)+3log_{3}(y)

simplify

5 lo g_{3} (x) + 3 lo g_{3} (y)

lo g_{3} (x^{5} y^{3})

Solution steps

5 lo g_{3} (x) + 3 lo g_{3} (y)

Apply log rule:

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

5 lo g_{3} (x) = lo g_{3} (x^{5})

= lo g_{3} (x^{5}) + 3 lo g_{3} (y)

Apply log rule:

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

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

= lo g_{3} (x^{5}) + lo g_{3} (y^{3})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{3} (x^{5}) + lo g_{3} (y^{3}) = lo g_{3} (x^{5} y^{3})

= lo g_{3} (x^{5} y^{3})

ln (\frac{40}{11})

ln (x + y) + ln (x - y) + ln (x^{6})

ln (\frac{- y + 4}{y + 3})

ln (x) + ln (1 + x)

ln (\frac{13}{23})

What is 5log_{3}(x)+3log_{3}(y) ?
The solution to 5log_{3}(x)+3log_{3}(y) is log_{3}(x^5y^3)