What is 1/2 ln(2(7)+1)+2ln(7-1)+c ?

The solution to 1/2 ln(2(7)+1)+2ln(7-1)+c is ln(36*15^{1/2})+c

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simplify 1/2 ln(2(7)+1)+2ln(7-1)+c

simplify

\frac{1}{2} ln (2 (7) + 1) + 2 ln (7 - 1) + c

ln (36 \cdot 1 5^{\frac{1}{2}}) + c

Solution steps

\frac{1}{2} ln (2 (7) + 1) + 2 ln (7 - 1) + c

Apply log rule:

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

\frac{1}{2} ln (2 (7) + 1) = ln ((2 (7) + 1)^{\frac{1}{2}})

= ln ((2 (7) + 1)^{\frac{1}{2}}) + 2 ln (7 - 1) + c

Apply log rule:

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

2 ln (7 - 1) = ln ((7 - 1)^{2})

= ln ((2 (7) + 1)^{\frac{1}{2}}) + ln ((7 - 1)^{2}) + c

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((2 (7) + 1)^{\frac{1}{2}}) + ln ((7 - 1)^{2}) = ln ((7 - 1)^{2} (2 \cdot 7 + 1)^{\frac{1}{2}})

= ln ((7 - 1)^{2} (2 \cdot 7 + 1)^{\frac{1}{2}}) + c

(2 (7) + 1)^{\frac{1}{2}} (7 - 1)^{2} = 36 \cdot 1 5^{\frac{1}{2}}

= ln (36 \cdot 1 5^{\frac{1}{2}}) + c

ln^{2} (5 x) + 3

(3 lo g_{10} (x) + 2 lo g_{10} (y)) - 6 lo g_{10} (z)

2 ln (x + 13) - ln (x + 7)

ln (\frac{0.0205}{0.02})

lo g_{10} (\frac{2 x}{y})

What is 1/2 ln(2(7)+1)+2ln(7-1)+c ?
The solution to 1/2 ln(2(7)+1)+2ln(7-1)+c is ln(36*15^{1/2})+c