What is 3log_{5}(a)+3log_{5}(b) ?

The solution to 3log_{5}(a)+3log_{5}(b) is log_{5}(a^3b^3)

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simplify 3log_{5}(a)+3log_{5}(b)

simplify

3 lo g_{5} (a) + 3 lo g_{5} (b)

lo g_{5} (a^{3} b^{3})

Solution steps

3 lo g_{5} (a) + 3 lo g_{5} (b)

Apply log rule:

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

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

= lo g_{5} (a^{3}) + 3 lo g_{5} (b)

Apply log rule:

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

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

= lo g_{5} (a^{3}) + lo g_{5} (b^{3})

Apply log rule:

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

lo g_{5} (a^{3}) + lo g_{5} (b^{3}) = lo g_{5} (a^{3} b^{3})

= lo g_{5} (a^{3} b^{3})

- lo g_{10} (1.14 \cdot 1 0^{- 4})

\frac{1}{2} lo g_{3} (7)

ln (\frac{1}{1 + e ^{- 1}})

72 ln (4) - 72 ln (6)

ln (x - 3) + ln (x + 2)

What is 3log_{5}(a)+3log_{5}(b) ?
The solution to 3log_{5}(a)+3log_{5}(b) is log_{5}(a^3b^3)