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

The solution to 1/2 ln|2(9)+1|+2ln|9-1| is ln(64*19^{1/2})

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

simplify

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

ln (64 \cdot 1 9^{\frac{1}{2}})

Decimal Notation

5.63110 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

2 ln ∣ 9 - 1 ∣ = ln (∣ 9 - 1 ∣^{2})

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

∣ 2 (9) + 1 ∣^{\frac{1}{2}} ∣ 9 - 1 ∣^{2} = 64 \cdot 1 9^{\frac{1}{2}}

= ln (64 \cdot 1 9^{\frac{1}{2}})

ln (\frac{1643.85}{547.85}) \cdot 8

ln (\frac{3.1416}{3})

7 ln (x + 7) - 9 ln (x)

lo g_{2} (8 x y)

ln (\frac{x ^{2}}{y ^{2}})

What is 1/2 ln|2(9)+1|+2ln|9-1| ?
The solution to 1/2 ln|2(9)+1|+2ln|9-1| is ln(64*19^{1/2})