What is log_{4}((a(x+3)^3)/(a-b^3)) ?

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

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simplify log_{4}((a(x+3)^3)/(a-b^3))

simplify

lo g_{4} (\frac{a ( x + 3 ) ^{3}}{a - b ^{3}})

lo g_{4} (a) + 3 lo g_{4} (x + 3) - lo g_{4} (a - b^{3})

Solution steps

lo g_{4} (\frac{a ( x + 3 ) ^{3}}{a - b ^{3}})

Apply log rule:

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

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

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

Simplify

lo g_{4} (a (x + 3)^{3}) : lo g_{4} (a) + 3 lo g_{4} (x + 3)

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

\frac{1}{2} ln (y) + ln (z)

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

2 lo g_{10} (8) + lo g_{10} (9) - lo g_{10} (36)

lo g_{b} (\frac{5}{3})

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

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