What is simplify-ln|6.1-3|+2ln|6.1-2|+c ?

The solution to simplify-ln|6.1-3|+2ln|6.1-2|+c is ln(5.42258…)+c

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simplify-ln|6.1-3|+2ln|6.1-2|+c

simplify

- ln ∣ 6.1 - 3 ∣ + 2 ln ∣ 6.1 - 2 ∣ + c

ln (5.42258 \dots) + c

Solution steps

- ln ∣ 6.1 - 3 ∣ + 2 ln ∣ 6.1 - 2 ∣ + c

Apply log rule:

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

2 ln ∣ 6.1 - 2 ∣ = ln (∣ 6.1 - 2 ∣^{2})

= - ln ∣ 6.1 - 3 ∣ + ln (∣ 6.1 - 2 ∣^{2}) + c

Apply log rule:

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

ln (∣ 6.1 - 2 ∣^{2}) - ln ∣ 6.1 - 3 ∣ = ln (\frac{∣ 6.1 - 2 ∣ ^{2}}{∣ 6.1 - 3 ∣})

= ln (\frac{∣ 6.1 - 2 ∣ ^{2}}{∣ 6.1 - 3 ∣}) + c

\frac{∣ 6.1 - 2 ∣ ^{2}}{∣ 6.1 - 3 ∣} = 5.42258 \dots

= ln (5.42258 \dots) + c

lo g_{2} (a) + \frac{1}{2} lo g_{2} (b) - 3 lo g_{2} (c)

- ln (4) + ln (5)

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- 30000 ln (\frac{49}{50})

- \frac{1}{3} ln (\frac{1}{3}) - \frac{1}{3} ln (\frac{1}{3}) - \frac{1}{3} ln (\frac{1}{3})

What is simplify-ln|6.1-3|+2ln|6.1-2|+c ?
The solution to simplify-ln|6.1-3|+2ln|6.1-2|+c is ln(5.42258…)+c