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

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

expand

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

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})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

ln (x) + \frac{4}{3} ln (y) - \frac{5}{3} ln (z) - \frac{1}{3} ln (x)

ln (\frac{6 x}{x ^{2} - 9})

lo g_{4} (19 b^{6} c)

ln (\frac{e ^{7}}{15})

lo g_{10} (x^{2}) - lo g_{10} (10 x)

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