What is log_{4}((x-2)/(x^5)) ?

The solution to log_{4}((x-2)/(x^5)) is log_{4}(x-2)-5log_{4}(x)

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simplify log_{4}((x-2)/(x^5))

simplify

lo g_{4} (\frac{x - 2}{x ^{5}})

lo g_{4} (x - 2) - 5 lo g_{4} (x)

Solution steps

lo g_{4} (\frac{x - 2}{x ^{5}})

Apply log rule:

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

lo g_{4} (\frac{x - 2}{x ^{5}}) = lo g_{4} (x - 2) - lo g_{4} (x^{5})

= lo g_{4} (x - 2) - lo g_{4} (x^{5})

Simplify

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

= lo g_{4} (x - 2) - 5 lo g_{4} (x)

lo g_{10} (\frac{1 0 ^{2} \cdot 1000}{x ^{3} \cdot y ^{- 2}})

lo g_{10} (\frac{10}{a ^{2} + b ^{2}})

5 lo g_{2} (x) + \frac{3}{4} lo g_{2} (y) - lo g_{2} (z)

5 lo g_{10} (x) - 8 lo g_{10} (x + 1)

What is log_{4}((x-2)/(x^5)) ?
The solution to log_{4}((x-2)/(x^5)) is log_{4}(x-2)-5log_{4}(x)