What is 1/2 ln|(8.7)+4|-1/2 ln|(8.7)+6|+C ?

The solution to 1/2 ln|(8.7)+4|-1/2 ln|(8.7)+6|+C is ln(0.92948…)+C

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simplify 1/2 ln|(8.7)+4|-1/2 ln|(8.7)+6|+C

simplify

\frac{1}{2} ln ∣ (8.7) + 4 ∣ - \frac{1}{2} ln ∣ (8.7) + 6 ∣ + C

ln (0.92948 \dots) + C

Solution steps

\frac{1}{2} ln ∣ (8.7) + 4 ∣ - \frac{1}{2} ln ∣ (8.7) + 6 ∣ + C

Apply log rule:

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

\frac{1}{2} ln ∣ 4 + (8.7) ∣ = ln (∣ 4 + (8.7) ∣^{\frac{1}{2}})

= ln (∣ 4 + (8.7) ∣^{\frac{1}{2}}) - \frac{1}{2} ln ∣ 6 + (8.7) ∣ + C

Apply log rule:

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

\frac{1}{2} ln ∣ 6 + (8.7) ∣ = ln (∣ 6 + (8.7) ∣^{\frac{1}{2}})

= ln (∣ 4 + (8.7) ∣^{\frac{1}{2}}) - ln (∣ 6 + (8.7) ∣^{\frac{1}{2}}) + C

Apply log rule:

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

ln (∣ (8.7) + 4 ∣^{\frac{1}{2}}) - ln (∣ (8.7) + 6 ∣^{\frac{1}{2}}) = ln (\frac{∣ 4 + 8.7 ∣ ^{\frac{1}{2}}}{∣ 6 + 8.7 ∣ ^{\frac{1}{2}}})

= ln (\frac{∣ 4 + 8.7 ∣ ^{\frac{1}{2}}}{∣ 6 + 8.7 ∣ ^{\frac{1}{2}}}) + C

\frac{∣ ( 8.7 ) + 4 ∣ ^{\frac{1}{2}}}{∣ ( 8.7 ) + 6 ∣ ^{\frac{1}{2}}} = 0.92948 \dots

= ln (0.92948 \dots) + C

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What is 1/2 ln|(8.7)+4|-1/2 ln|(8.7)+6|+C ?
The solution to 1/2 ln|(8.7)+4|-1/2 ln|(8.7)+6|+C is ln(0.92948…)+C