What is expand log_{b}((bsqrt(b))/((c+1)^3)) ?

The solution to expand log_{b}((bsqrt(b))/((c+1)^3)) is 1+log_{b}(sqrt(b))-3log_{b}(c+1)

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expand log_{b}((bsqrt(b))/((c+1)^3))

expand

lo g_{b} (\frac{b b}{( c + 1 ) ^{3}})

1 + lo g_{b} (b) - 3 lo g_{b} (c + 1)

Solution steps

lo g_{b} (\frac{b b}{( c + 1 ) ^{3}})

Apply log rule:

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

lo g_{b} (\frac{b b}{( c + 1 ) ^{3}}) = lo g_{b} (b b) - lo g_{b} ((c + 1)^{3})

= lo g_{b} (b b) - lo g_{b} ((c + 1)^{3})

Apply log rule:

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

lo g_{b} ((c + 1)^{3}) = 3 lo g_{b} (c + 1)

= lo g_{b} (b b) - 3 lo g_{b} (c + 1)

Apply log rule:

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

lo g_{b} (b b) = lo g_{b} (b) + lo g_{b} (b)

= lo g_{b} (b) + lo g_{b} (b) - 3 lo g_{b} (c + 1)

Apply log rule:

lo g_{a} (a) = 1

= 1 + lo g_{b} (b) - 3 lo g_{b} (c + 1)

2 ln (x) - 3 ln (x - 1) - ln (x)

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

lo g_{2} (32 x^{3})

lo g_{10} (2 x)

\frac{1}{3} [ln (x) + 2 ln (x + 4)] - ln (x - 1)

What is expand log_{b}((bsqrt(b))/((c+1)^3)) ?
The solution to expand log_{b}((bsqrt(b))/((c+1)^3)) is 1+log_{b}(sqrt(b))-3log_{b}(c+1)