What is 3log_{5}(a)+4log_{5}(b) ?

The solution to 3log_{5}(a)+4log_{5}(b) is log_{5}(a^3b^4)

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simplify 3log_{5}(a)+4log_{5}(b)

simplify

3 lo g_{5} (a) + 4 lo g_{5} (b)

lo g_{5} (a^{3} b^{4})

Solution steps

3 lo g_{5} (a) + 4 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}) + 4 lo g_{5} (b)

Apply log rule:

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

4 lo g_{5} (b) = lo g_{5} (b^{4})

= lo g_{5} (a^{3}) + lo g_{5} (b^{4})

Apply log rule:

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

lo g_{5} (a^{3}) + lo g_{5} (b^{4}) = lo g_{5} (a^{3} b^{4})

= lo g_{5} (a^{3} b^{4})

2 ln (4) + 2 ln (3)

ln (\frac{4 x - 3}{x})

ln (x^{2} + 3 x) - ln (x^{2} + x)

ln (8) - 2 ln (4) + ln (15)

ln (27) - ln (9)

What is 3log_{5}(a)+4log_{5}(b) ?
The solution to 3log_{5}(a)+4log_{5}(b) is log_{5}(a^3b^4)