What is simplify-ln|8-3|+2ln|8-2| ?

The solution to simplify-ln|8-3|+2ln|8-2| is ln(36/5)

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simplify-ln|8-3|+2ln|8-2|

simplify

- ln ∣ 8 - 3 ∣ + 2 ln ∣ 8 - 2 ∣

ln (\frac{36}{5})

Decimal Notation

1.97408 \dots

Solution steps

- ln ∣ 8 - 3 ∣ + 2 ln ∣ 8 - 2 ∣

Apply log rule:

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

2 ln ∣ 8 - 2 ∣ = ln (∣ 8 - 2 ∣^{2})

= - ln ∣ 8 - 3 ∣ + ln (∣ 8 - 2 ∣^{2})

Apply log rule:

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

ln (∣ 8 - 2 ∣^{2}) - ln ∣ 8 - 3 ∣ = ln (\frac{∣ 8 - 2 ∣ ^{2}}{∣ 8 - 3 ∣})

= ln (\frac{∣ 8 - 2 ∣ ^{2}}{∣ 8 - 3 ∣})

\frac{∣ 8 - 2 ∣ ^{2}}{∣ 8 - 3 ∣} = \frac{36}{5}

= ln (\frac{36}{5})

\frac{1}{14} \cdot ln (129)

ln (\frac{3}{11})

2 lo g_{10} (x) + 7 lo g_{10} (x - 9)

1.005 \cdot ln (1.687) - 0.287 \cdot ln (4.5)

ln^{2} (x) + 2 ln (x)

What is simplify-ln|8-3|+2ln|8-2| ?
The solution to simplify-ln|8-3|+2ln|8-2| is ln(36/5)