What is ln((x^2+1)(x^3+2)^6) ?

The solution to ln((x^2+1)(x^3+2)^6) is ln(x^2+1)+6ln(x^3+2)

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simplify ln((x^2+1)(x^3+2)^6)

simplify

ln ((x^{2} + 1) (x^{3} + 2)^{6})

ln (x^{2} + 1) + 6 ln (x^{3} + 2)

Solution steps

ln ((x^{2} + 1) (x^{3} + 2)^{6})

Apply log rule:

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

ln ((x^{2} + 1) (x^{3} + 2)^{6}) = ln (x^{2} + 1) + ln ((x^{3} + 2)^{6})

= ln (x^{2} + 1) + ln ((x^{3} + 2)^{6})

Apply log rule:

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

ln ((x^{3} + 2)^{6}) = 6 ln (x^{3} + 2)

= ln (x^{2} + 1) + 6 ln (x^{3} + 2)

[5 lo g_{7} (2) + 3 lo g_{7} (m - 2)]

lo g_{4} (1 e^{20})

\frac{d}{d x} (\frac{1}{x ^{2} + 1}) + ln (\frac{1}{x})

\frac{7}{30} (ln (7) - ln (2))

lo g_{2} (x - 3) + lo g_{2} (x - 1)

What is ln((x^2+1)(x^3+2)^6) ?
The solution to ln((x^2+1)(x^3+2)^6) is ln(x^2+1)+6ln(x^3+2)