What is ln((1+x)^3(2x-5)^6) ?

The solution to ln((1+x)^3(2x-5)^6) is 3ln(1+x)+6ln(2x-5)

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simplify ln((1+x)^3(2x-5)^6)

simplify

ln ((1 + x)^{3} (2 x - 5)^{6})

3 ln (1 + x) + 6 ln (2 x - 5)

Solution steps

ln ((1 + x)^{3} (2 x - 5)^{6})

Apply log rule:

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

ln ((1 + x)^{3} (2 x - 5)^{6}) = ln ((1 + x)^{3}) + ln ((2 x - 5)^{6})

= ln ((x + 1)^{3}) + ln ((2 x - 5)^{6})

Apply log rule:

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

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

= 3 ln (1 + x) + ln ((2 x - 5)^{6})

Apply log rule:

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

ln ((2 x - 5)^{6}) = 6 ln (2 x - 5)

= 3 ln (1 + x) + 6 ln (2 x - 5)

2 (ln (x) - ln (x + 3) - ln (x - 3))

ln (\frac{7 x + 1}{2})

\frac{ln ( 4 x + 7 ) - ln ( 7 )}{x}

ln (- 3 e^{- 2 x})

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

What is ln((1+x)^3(2x-5)^6) ?
The solution to ln((1+x)^3(2x-5)^6) is 3ln(1+x)+6ln(2x-5)