What is log_{3}((x^4)/(y^{3/5)}) ?

The solution to log_{3}((x^4)/(y^{3/5)}) is 4log_{3}(x)-3/5 log_{3}(y)

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simplify log_{3}((x^4)/(y^{3/5)})

simplify

lo g_{3} (\frac{x ^{4}}{y ^{\frac{3}{5}}})

4 lo g_{3} (x) - \frac{3}{5} lo g_{3} (y)

Solution steps

lo g_{3} (\frac{x ^{4}}{y ^{\frac{3}{5}}})

Apply log rule:

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

lo g_{3} (\frac{x ^{4}}{y ^{\frac{3}{5}}}) = lo g_{3} (x^{4}) - lo g_{3} (y^{\frac{3}{5}})

= lo g_{3} (x^{4}) - lo g_{3} (y^{\frac{3}{5}})

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

lo g_{3} (y^{\frac{3}{5}}) = \frac{3}{5} lo g_{3} (y)

= 4 lo g_{3} (x) - \frac{3}{5} lo g_{3} (y)

lo g_{4} (3) + lo g_{4} (10)

\frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{5 ln ( 7 ) - ln ( 2 )}

ln (\frac{A}{B})

lo g_{9} (x) + lo g_{9} (x + 8)

lo g_{10} (x^{9} z)

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