What is 1/2 ln(4x+1)-ln(8) ?

The solution to 1/2 ln(4x+1)-ln(8) is ln(((4x+1)^{1/2})/8)

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

ln (\frac{270}{1 0 ^{5}})

lo g_{10} (\frac{3 a}{4})

ln (\frac{( 3 x - 5 )}{7})

ln (a \cdot e^{- \frac{x}{5}})

ln (2 n) + n

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