What is simplify-ln|5.1-3|+2ln|5.1-2| ?

The solution to simplify-ln|5.1-3|+2ln|5.1-2| is ln(4.57619…)

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simplify-ln|5.1-3|+2ln|5.1-2|

simplify

- ln ∣ 5.1 - 3 ∣ + 2 ln ∣ 5.1 - 2 ∣

ln (4.57619 \dots)

Decimal

1.52086 \dots

Solution steps

- ln ∣ 5.1 - 3 ∣ + 2 ln ∣ 5.1 - 2 ∣

Apply log rule:

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

2 ln ∣ 5.1 - 2 ∣ = ln (∣ 5.1 - 2 ∣^{2})

= - ln ∣ 5.1 - 3 ∣ + ln (∣ 5.1 - 2 ∣^{2})

Apply log rule:

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

ln (∣ 5.1 - 2 ∣^{2}) - ln ∣ 5.1 - 3 ∣ = ln (\frac{∣ 5.1 - 2 ∣ ^{2}}{∣ 5.1 - 3 ∣})

= ln (\frac{∣ 5.1 - 2 ∣ ^{2}}{∣ 5.1 - 3 ∣})

\frac{∣ 5.1 - 2 ∣ ^{2}}{∣ 5.1 - 3 ∣} = 4.57619 \dots

= ln (4.57619 \dots)

2 ln (x) + 3 ln (1 + x) - 4 ln (2 + x)

ln (\frac{463.15}{343.15})

lo g_{2} (\frac{x ^{3}}{9 y})

- lo g_{10} (3 \cdot 1 0^{- 9})

ln (1 - x - y) - ln (x)

What is simplify-ln|5.1-3|+2ln|5.1-2| ?
The solution to simplify-ln|5.1-3|+2ln|5.1-2| is ln(4.57619…)