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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (\frac{e ^{- y} y ^{x}}{x !})

ln (\frac{x}{1200 - x})

ln (43)

\frac{ln ( 9 ) - 6 ln ( 6 ) + 6 ln ( 2 )}{2}

ln (\frac{2 i - 3}{2 i + 3})

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