What is 2log_{5}(m)-3log_{5}(n) ?

The solution to 2log_{5}(m)-3log_{5}(n) is log_{5}((m^2)/(n^3))

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simplify 2log_{5}(m)-3log_{5}(n)

simplify

2 lo g_{5} (m) - 3 lo g_{5} (n)

lo g_{5} (\frac{m ^{2}}{n ^{3}})

Solution steps

2 lo g_{5} (m) - 3 lo g_{5} (n)

Apply log rule:

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

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

= lo g_{5} (m^{2}) - 3 lo g_{5} (n)

Apply log rule:

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

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

= lo g_{5} (m^{2}) - lo g_{5} (n^{3})

Apply log rule:

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

lo g_{5} (m^{2}) - lo g_{5} (n^{3}) = lo g_{5} (\frac{m ^{2}}{n ^{3}})

= lo g_{5} (\frac{m ^{2}}{n ^{3}})

\frac{1}{2} ln (x^{2} + 9) + ln (\frac{3}{x ^{2} + 9})

ln (3) + ln (2 x - 1) - ln (4) - ln (x + 1)

\frac{1}{2} ln (10 x)

ln (\frac{162}{e})

4 lo g_{2} (x + 8) - lo g_{2} (x - 9) - lo g_{2} (x - 8)

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