What is log_{5}((a^3)/(b^2)) ?

The solution to log_{5}((a^3)/(b^2)) is 3log_{5}(a)-2log_{5}(b)

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simplify log_{5}((a^3)/(b^2))

simplify

lo g_{5} (\frac{a ^{3}}{b ^{2}})

3 lo g_{5} (a) - 2 lo g_{5} (b)

Solution steps

lo g_{5} (\frac{a ^{3}}{b ^{2}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{5} (\frac{a ^{3}}{b ^{2}}) = lo g_{5} (a^{3}) - lo g_{5} (b^{2})

= lo g_{5} (a^{3}) - lo g_{5} (b^{2})

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

lo g_{5} (b^{2}) = 2 lo g_{5} (b)

= 3 lo g_{5} (a) - 2 lo g_{5} (b)

\frac{1}{2} (lo g_{6} (x) + lo g_{6} (y))

- lo g_{10} (3.3 \cdot 1 0^{- 6})

2 lo g_{a} (3) - 2 lo g_{a} (2)

ln (2) - ln (x)

\frac{1}{4} ln (x) + 5 [ln (x - 2) - \frac{3}{10} ln (x + 2)]

What is log_{5}((a^3)/(b^2)) ?
The solution to log_{5}((a^3)/(b^2)) is 3log_{5}(a)-2log_{5}(b)