What is 1/2 ln(2(7.1)+1)+2ln(7.1-1) ?

The solution to 1/2 ln(2(7.1)+1)+2ln(7.1-1) is ln(145.07128…)

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simplify 1/2 ln(2(7.1)+1)+2ln(7.1-1)

simplify

\frac{1}{2} ln (2 (7.1) + 1) + 2 ln (7.1 - 1)

ln (145.07128 \dots)

Decimal Notation

4.97722 \dots

Solution steps

\frac{1}{2} ln (2 (7.1) + 1) + 2 ln (7.1 - 1)

Apply log rule:

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

\frac{1}{2} ln (2 (7.1) + 1) = ln ((2 (7.1) + 1)^{\frac{1}{2}})

= ln ((2 (7.1) + 1)^{\frac{1}{2}}) + 2 ln (7.1 - 1)

Apply log rule:

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

2 ln (7.1 - 1) = ln ((7.1 - 1)^{2})

= ln ((2 (7.1) + 1)^{\frac{1}{2}}) + ln ((7.1 - 1)^{2})

Apply log rule:

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

ln ((2 (7.1) + 1)^{\frac{1}{2}}) + ln ((7.1 - 1)^{2}) = ln ((7.1 - 1)^{2} (2 \cdot 7.1 + 1)^{\frac{1}{2}})

= ln ((7.1 - 1)^{2} (2 \cdot 7.1 + 1)^{\frac{1}{2}})

(2 (7.1) + 1)^{\frac{1}{2}} (7.1 - 1)^{2} = 145.07128 \dots

= ln (145.07128 \dots)

6 (\frac{1}{5} ln ∣ z - 1 ∣ - \frac{1}{5} ln ∣ z + 4 ∣)

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

- ln (i - n) + ln (i)

3 ln (\frac{3}{2})

ln (t) + ln (t + 6) + ln (t + 4)

What is 1/2 ln(2(7.1)+1)+2ln(7.1-1) ?
The solution to 1/2 ln(2(7.1)+1)+2ln(7.1-1) is ln(145.07128…)