What is simplify-1/2 ln|(9)+1|+1/2 ln|(9)-1| ?

The solution to simplify-1/2 ln|(9)+1|+1/2 ln|(9)-1| is ln((2sqrt(5))/5)

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simplify-1/2 ln|(9)+1|+1/2 ln|(9)-1|

simplify

- \frac{1}{2} ln ∣ (9) + 1 ∣ + \frac{1}{2} ln ∣ (9) - 1 ∣

ln (\frac{2 5}{5})

Decimal Notation

- 0.11157 \dots

Solution steps

- \frac{1}{2} ln ∣ (9) + 1 ∣ + \frac{1}{2} ln ∣ (9) - 1 ∣

Apply log rule:

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

\frac{1}{2} ln ∣ (9) + 1 ∣ = ln (∣ (9) + 1 ∣^{\frac{1}{2}})

= - ln (∣ (9) + 1 ∣^{\frac{1}{2}}) + \frac{1}{2} ln ∣ (9) - 1 ∣

Apply log rule:

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

\frac{1}{2} ln ∣ (9) - 1 ∣ = ln (∣ (9) - 1 ∣^{\frac{1}{2}})

= - ln (∣ (9) + 1 ∣^{\frac{1}{2}}) + ln (∣ (9) - 1 ∣^{\frac{1}{2}})

Apply log rule:

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

ln (∣ (9) - 1 ∣^{\frac{1}{2}}) - ln (∣ (9) + 1 ∣^{\frac{1}{2}}) = ln (\frac{∣ 9 - 1 ∣ ^{\frac{1}{2}}}{∣ 9 + 1 ∣ ^{\frac{1}{2}}})

= ln (\frac{∣ 9 - 1 ∣ ^{\frac{1}{2}}}{∣ 9 + 1 ∣ ^{\frac{1}{2}}})

\frac{∣ ( 9 ) - 1 ∣ ^{\frac{1}{2}}}{∣ ( 9 ) + 1 ∣ ^{\frac{1}{2}}} = \frac{2 5}{5}

= ln (\frac{2 5}{5})

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What is simplify-1/2 ln|(9)+1|+1/2 ln|(9)-1| ?
The solution to simplify-1/2 ln|(9)+1|+1/2 ln|(9)-1| is ln((2sqrt(5))/5)