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Popular >

simplify ln(((4x+1)^2)/8)

Solution

simplify

ln (\frac{( 4 x + 1 ) ^{2}}{8})

Solution

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

Solution steps

ln (\frac{( 4 x + 1 ) ^{2}}{8})

Apply log rule:

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

ln (\frac{( 4 x + 1 ) ^{2}}{8}) = ln ((4 x + 1)^{2}) - ln (8)

= ln ((4 x + 1)^{2}) - ln (8)

Apply log rule:

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

ln ((4 x + 1)^{2}) = 2 ln (4 x + 1)

= 2 ln (4 x + 1) - ln (8)

ln (8) = 3 ln (2)

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

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Frequently Asked Questions (FAQ)

What is ln(((4x+1)^2)/8) ?
The solution to ln(((4x+1)^2)/8) is 2ln(4x+1)-3ln(2)