What is ln(((3x-8)^2)/(5x+1)) ?

The solution to ln(((3x-8)^2)/(5x+1)) is 2ln(3x-8)-ln(5x+1)

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simplify ln(((3x-8)^2)/(5x+1))

simplify

ln (\frac{( 3 x - 8 ) ^{2}}{5 x + 1})

2 ln (3 x - 8) - ln (5 x + 1)

Solution steps

ln (\frac{( 3 x - 8 ) ^{2}}{5 x + 1})

Apply log rule:

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

ln (\frac{( 3 x - 8 ) ^{2}}{5 x + 1}) = ln ((3 x - 8)^{2}) - ln (5 x + 1)

= ln ((3 x - 8)^{2}) - ln (5 x + 1)

Apply log rule:

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

ln ((3 x - 8)^{2}) = 2 ln (3 x - 8)

= 2 ln (3 x - 8) - ln (5 x + 1)

2 lo g_{\frac{16}{3}} (6)

lo g_{10} (5 \cdot 1 0^{- 2})

ln (\frac{0.25}{9})

\frac{1}{9} ln (3)

ln ((- 1) (3))

What is ln(((3x-8)^2)/(5x+1)) ?
The solution to ln(((3x-8)^2)/(5x+1)) is 2ln(3x-8)-ln(5x+1)