What is 7/2 ln|2(0.5-3)|-7/2 ln|2(-0.5-3)| ?

The solution to 7/2 ln|2(0.5-3)|-7/2 ln|2(-0.5-3)| is ln(0.30800…)

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simplify 7/2 ln|2(0.5-3)|-7/2 ln|2(-0.5-3)|

simplify

\frac{7}{2} ln ∣ 2 (0.5 - 3) ∣ - \frac{7}{2} ln ∣ 2 (- 0.5 - 3) ∣

ln (0.30800 \dots)

Decimal Notation

- 1.17765 \dots

Solution steps

\frac{7}{2} ln ∣ 2 (0.5 - 3) ∣ - \frac{7}{2} ln ∣ 2 (- 0.5 - 3) ∣

Apply log rule:

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

\frac{7}{2} ln ∣ 2 (0.5 - 3) ∣ = ln (∣ 2 (0.5 - 3) ∣^{\frac{7}{2}})

= ln (∣ 2 (0.5 - 3) ∣^{\frac{7}{2}}) - \frac{7}{2} ln ∣ 2 (- 3 - 0.5) ∣

Apply log rule:

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

\frac{7}{2} ln ∣ 2 (- 3 - 0.5) ∣ = ln (∣ 2 (- 3 - 0.5) ∣^{\frac{7}{2}})

= ln (∣ 2 (0.5 - 3) ∣^{\frac{7}{2}}) - ln (∣ 2 (- 3 - 0.5) ∣^{\frac{7}{2}})

Apply log rule:

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

ln (∣ 2 (0.5 - 3) ∣^{\frac{7}{2}}) - ln (∣ 2 (- 0.5 - 3) ∣^{\frac{7}{2}}) = ln (\frac{∣ 2 ( 0.5 - 3 ) ∣ ^{\frac{7}{2}}}{∣ 2 ( - 3 - 0.5 ) ∣ ^{\frac{7}{2}}})

= ln (\frac{∣ 2 ( 0.5 - 3 ) ∣ ^{\frac{7}{2}}}{∣ 2 ( - 0.5 - 3 ) ∣ ^{\frac{7}{2}}})

\frac{∣ 2 ( 0.5 - 3 ) ∣ ^{\frac{7}{2}}}{∣ 2 ( - 0.5 - 3 ) ∣ ^{\frac{7}{2}}} = 0.30800 \dots

= ln (0.30800 \dots)

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 7)

- \frac{3}{4} lo g_{e} (\frac{3}{4}) - \frac{1}{4} lo g_{e} (\frac{1}{4})

ln (41) - ln (5) - ln (2)

lo g_{7} (\frac{ln ( 0.25 )}{ln ( 0.75 )})

2 ln (\frac{308.15}{298.15})

What is 7/2 ln|2(0.5-3)|-7/2 ln|2(-0.5-3)| ?
The solution to 7/2 ln|2(0.5-3)|-7/2 ln|2(-0.5-3)| is ln(0.30800…)