What is ln(((2t+1)^3)/((3t-1)^4)) ?

The solution to ln(((2t+1)^3)/((3t-1)^4)) is 3ln(2t+1)-4ln(3t-1)

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simplify ln(((2t+1)^3)/((3t-1)^4))

simplify

ln (\frac{( 2 t + 1 ) ^{3}}{( 3 t - 1 ) ^{4}})

3 ln (2 t + 1) - 4 ln (3 t - 1)

Solution steps

ln (\frac{( 2 t + 1 ) ^{3}}{( 3 t - 1 ) ^{4}})

Apply log rule:

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

ln (\frac{( 2 t + 1 ) ^{3}}{( 3 t - 1 ) ^{4}}) = ln ((2 t + 1)^{3}) - ln ((3 t - 1)^{4})

= ln ((2 t + 1)^{3}) - ln ((3 t - 1)^{4})

Apply log rule:

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

ln ((2 t + 1)^{3}) = 3 ln (2 t + 1)

= 3 ln (2 t + 1) - ln ((3 t - 1)^{4})

Apply log rule:

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

ln ((3 t - 1)^{4}) = 4 ln (3 t - 1)

= 3 ln (2 t + 1) - 4 ln (3 t - 1)

ln (\frac{1}{a} e^{- \frac{x}{a}})

8 lo g_{e} (2 x) - lo g_{e} (2)

lo g_{2} ((x^{3} + 2) (x - 4)^{3})

lo g_{10} (5 \cdot 1 0^{- 3})

ln ((x + 1)^{2} m)

What is ln(((2t+1)^3)/((3t-1)^4)) ?
The solution to ln(((2t+1)^3)/((3t-1)^4)) is 3ln(2t+1)-4ln(3t-1)