What is 1/2 ln(17.6+1)+2ln(8.8-1)+C ?

The solution to 1/2 ln(17.6+1)+2ln(8.8-1)+C is ln(262.38903…)+C

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simplify 1/2 ln(17.6+1)+2ln(8.8-1)+C

simplify

\frac{1}{2} ln (17.6 + 1) + 2 ln (8.8 - 1) + C

ln (262.38903 \dots) + C

Solution steps

\frac{1}{2} ln (17.6 + 1) + 2 ln (8.8 - 1) + C

Apply log rule:

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

\frac{1}{2} ln (1 + 17.6) = ln ((1 + 17.6)^{\frac{1}{2}})

= ln ((1 + 17.6)^{\frac{1}{2}}) + 2 ln (8.8 - 1) + C

Apply log rule:

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

2 ln (8.8 - 1) = ln ((8.8 - 1)^{2})

= ln ((1 + 17.6)^{\frac{1}{2}}) + ln ((8.8 - 1)^{2}) + C

Apply log rule:

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

ln ((17.6 + 1)^{\frac{1}{2}}) + ln ((8.8 - 1)^{2}) = ln ((8.8 - 1)^{2} (1 + 17.6)^{\frac{1}{2}})

= ln ((8.8 - 1)^{2} (1 + 17.6)^{\frac{1}{2}}) + C

(17.6 + 1)^{\frac{1}{2}} (8.8 - 1)^{2} = 262.38903 \dots

= ln (262.38903 \dots) + C

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What is 1/2 ln(17.6+1)+2ln(8.8-1)+C ?
The solution to 1/2 ln(17.6+1)+2ln(8.8-1)+C is ln(262.38903…)+C