What is log_{4}((x^5)/(y^8)) ?

The solution to log_{4}((x^5)/(y^8)) is 5log_{4}(x)-8log_{4}(y)

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simplify log_{4}((x^5)/(y^8))

simplify

lo g_{4} (\frac{x ^{5}}{y ^{8}})

5 lo g_{4} (x) - 8 lo g_{4} (y)

Solution steps

lo g_{4} (\frac{x ^{5}}{y ^{8}})

Apply log rule:

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

lo g_{4} (\frac{x ^{5}}{y ^{8}}) = lo g_{4} (x^{5}) - lo g_{4} (y^{8})

= lo g_{4} (x^{5}) - lo g_{4} (y^{8})

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

lo g_{4} (y^{8}) = 8 lo g_{4} (y)

= 5 lo g_{4} (x) - 8 lo g_{4} (y)

lo g_{2} (3) + lo g_{2} (5) + lo g_{2} (x - 2)

lo g_{10} (x (x^{2} + 2)^{\frac{1}{2}})

ln (x) - 3 [ln (x - 6) + ln (x + 6)]

lo g_{3} (\frac{y}{27})

lo g_{10} (\frac{27}{y})

What is log_{4}((x^5)/(y^8)) ?
The solution to log_{4}((x^5)/(y^8)) is 5log_{4}(x)-8log_{4}(y)