What is 3log_{9}(a)-12log_{9}(b) ?

The solution to 3log_{9}(a)-12log_{9}(b) is log_{9}((a^3)/(b^{12)})

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simplify 3log_{9}(a)-12log_{9}(b)

simplify

3 lo g_{9} (a) - 12 lo g_{9} (b)

lo g_{9} (\frac{a ^{3}}{b ^{12}})

Solution steps

3 lo g_{9} (a) - 12 lo g_{9} (b)

Apply log rule:

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

3 lo g_{9} (a) = lo g_{9} (a^{3})

= lo g_{9} (a^{3}) - 12 lo g_{9} (b)

Apply log rule:

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

12 lo g_{9} (b) = lo g_{9} (b^{12})

= lo g_{9} (a^{3}) - lo g_{9} (b^{12})

Apply log rule:

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

lo g_{9} (a^{3}) - lo g_{9} (b^{12}) = lo g_{9} (\frac{a ^{3}}{b ^{12}})

= lo g_{9} (\frac{a ^{3}}{b ^{12}})

3 ln ∣ x ∣ - 2 ln ∣ x + 11 ∣

\frac{3}{2} ln (t) + \frac{1}{2} ln (b) - 2 + ln (e^{2}) - 8 ln (m)

ln (800 e^{0.05 t}) - ln (220 e^{- 0.05 t})

ln (e^{4 x} x^{7})

ln ((3 - 2 x)^{t a n (\frac{3 π x}{2})})

What is 3log_{9}(a)-12log_{9}(b) ?
The solution to 3log_{9}(a)-12log_{9}(b) is log_{9}((a^3)/(b^{12)})