What is 36log_{3}(a)-6log_{3}(b) ?

The solution to 36log_{3}(a)-6log_{3}(b) is log_{3}((a^{36})/(b^6))

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simplify 36log_{3}(a)-6log_{3}(b)

simplify

36 lo g_{3} (a) - 6 lo g_{3} (b)

lo g_{3} (\frac{a ^{36}}{b ^{6}})

Solution steps

36 lo g_{3} (a) - 6 lo g_{3} (b)

Apply log rule:

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

36 lo g_{3} (a) = lo g_{3} (a^{36})

= lo g_{3} (a^{36}) - 6 lo g_{3} (b)

Apply log rule:

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

6 lo g_{3} (b) = lo g_{3} (b^{6})

= lo g_{3} (a^{36}) - lo g_{3} (b^{6})

Apply log rule:

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

lo g_{3} (a^{36}) - lo g_{3} (b^{6}) = lo g_{3} (\frac{a ^{36}}{b ^{6}})

= lo g_{3} (\frac{a ^{36}}{b ^{6}})

lo g_{10} (5 \cdot 1 0^{- 4})

\frac{ln ( 5 )}{2 ln ( 3 )} - 9

ln (\frac{x}{y ^{3}}) - 3 \cdot \frac{1}{y} + \frac{1}{2} \cdot ln (\frac{1}{x ^{4} y ^{2}})

\frac{ln ( \frac{21}{4} )}{5 ln ( 2 )}

ln (\frac{2}{3} e^{3 x})

What is 36log_{3}(a)-6log_{3}(b) ?
The solution to 36log_{3}(a)-6log_{3}(b) is log_{3}((a^{36})/(b^6))