What is 5-(-ln|8.7-3|+2ln|8.7-2|) ?

The solution to 5-(-ln|8.7-3|+2ln|8.7-2|) is 5-ln(7.87543…)

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simplify 5-(-ln|8.7-3|+2ln|8.7-2|)

simplify

5 - (- ln ∣ 8.7 - 3 ∣ + 2 ln ∣ 8.7 - 2 ∣)

5 - ln (7.87543 \dots)

Decimal Notation

2.93625 \dots

Solution steps

5 - (- ln ∣ 8.7 - 3 ∣ + 2 ln ∣ 8.7 - 2 ∣)

Apply log rule:

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

2 ln ∣ 8.7 - 2 ∣ = ln (∣ 8.7 - 2 ∣^{2})

= 5 - (ln (∣ 8.7 - 2 ∣^{2}) - ln ∣ 8.7 - 3 ∣)

Apply log rule:

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

ln (∣ 8.7 - 2 ∣^{2}) - ln ∣ 8.7 - 3 ∣ = ln (\frac{∣ 8.7 - 2 ∣ ^{2}}{∣ 8.7 - 3 ∣})

= 5 - (ln (\frac{∣ 8.7 - 2 ∣ ^{2}}{∣ 8.7 - 3 ∣}))

\frac{∣ 8.7 - 2 ∣ ^{2}}{∣ 8.7 - 3 ∣} = 7.87543 \dots

= 5 - (ln (7.87543 \dots))

Remove parentheses:

(a) = a

= 5 - ln (7.87543 \dots)

ln (\frac{0.2031}{0.2609})

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ln (\frac{4.08 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}})

ln (\frac{1 - ( 2 )}{2 + 1})

- \frac{ln ( 6 )}{4 ln ( 2 )}

What is 5-(-ln|8.7-3|+2ln|8.7-2|) ?
The solution to 5-(-ln|8.7-3|+2ln|8.7-2|) is 5-ln(7.87543…)