What is 1/2 ln|2(8.5)+1|+2ln|8.5-1|+c ?

The solution to 1/2 ln|2(8.5)+1|+2ln|8.5-1|+c is ln(238.64853…)+c

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simplify 1/2 ln|2(8.5)+1|+2ln|8.5-1|+c

simplify

\frac{1}{2} ln ∣ 2 (8.5) + 1 ∣ + 2 ln ∣ 8.5 - 1 ∣ + c

ln (238.64853 \dots) + c

Solution steps

\frac{1}{2} ln ∣ 2 (8.5) + 1 ∣ + 2 ln ∣ 8.5 - 1 ∣ + c

Apply log rule:

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

\frac{1}{2} ln ∣ 2 (8.5) + 1 ∣ = ln (∣ 2 (8.5) + 1 ∣^{\frac{1}{2}})

= ln (∣ 2 (8.5) + 1 ∣^{\frac{1}{2}}) + 2 ln ∣ 8.5 - 1 ∣ + c

Apply log rule:

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

2 ln ∣ 8.5 - 1 ∣ = ln (∣ 8.5 - 1 ∣^{2})

= ln (∣ 2 (8.5) + 1 ∣^{\frac{1}{2}}) + ln (∣ 8.5 - 1 ∣^{2}) + c

Apply log rule:

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

ln (∣ 2 (8.5) + 1 ∣^{\frac{1}{2}}) + ln (∣ 8.5 - 1 ∣^{2}) = ln (∣ 8.5 - 1 ∣^{2} ∣ 2 \cdot 8.5 + 1 ∣^{\frac{1}{2}})

= ln (∣ 8.5 - 1 ∣^{2} ∣ 2 \cdot 8.5 + 1 ∣^{\frac{1}{2}}) + c

∣ 2 (8.5) + 1 ∣^{\frac{1}{2}} ∣ 8.5 - 1 ∣^{2} = 238.64853 \dots

= ln (238.64853 \dots) + c

ln (\frac{x ^{2} + y ^{2} - x}{x ^{2} + y ^{2} + x})

ln (\frac{1}{80})

ln (\frac{2 a}{b})

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

ln (\frac{52}{62})

What is 1/2 ln|2(8.5)+1|+2ln|8.5-1|+c ?
The solution to 1/2 ln|2(8.5)+1|+2ln|8.5-1|+c is ln(238.64853…)+c