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

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

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

simplify

ln (\frac{2 x + 1}{( 3 x + 1 ) ^{2}})

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

Solution steps

ln (\frac{2 x + 1}{( 3 x + 1 ) ^{2}})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- ln (2) \cdot \frac{1}{20}

ln (\frac{69.61}{70.586})

8 ln (c) + 8 ln (x)

ln (20 x)

3 ln (1.75) - ln (- 0.5) + ln (- 1) + 6

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