What is 1/2 ln(2(9.5)+1)+2ln(9.5-1) ?

The solution to 1/2 ln(2(9.5)+1)+2ln(9.5-1) is ln(323.11182…)

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simplify 1/2 ln(2(9.5)+1)+2ln(9.5-1)

simplify

\frac{1}{2} ln (2 (9.5) + 1) + 2 ln (9.5 - 1)

ln (323.11182 \dots)

Decimal Notation

5.77799 \dots

Solution steps

\frac{1}{2} ln (2 (9.5) + 1) + 2 ln (9.5 - 1)

Apply log rule:

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

\frac{1}{2} ln (2 (9.5) + 1) = ln ((2 (9.5) + 1)^{\frac{1}{2}})

= ln ((2 (9.5) + 1)^{\frac{1}{2}}) + 2 ln (9.5 - 1)

Apply log rule:

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

2 ln (9.5 - 1) = ln ((9.5 - 1)^{2})

= ln ((2 (9.5) + 1)^{\frac{1}{2}}) + ln ((9.5 - 1)^{2})

Apply log rule:

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

ln ((2 (9.5) + 1)^{\frac{1}{2}}) + ln ((9.5 - 1)^{2}) = ln ((9.5 - 1)^{2} (2 \cdot 9.5 + 1)^{\frac{1}{2}})

= ln ((9.5 - 1)^{2} (2 \cdot 9.5 + 1)^{\frac{1}{2}})

(2 (9.5) + 1)^{\frac{1}{2}} (9.5 - 1)^{2} = 323.11182 \dots

= ln (323.11182 \dots)

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What is 1/2 ln(2(9.5)+1)+2ln(9.5-1) ?
The solution to 1/2 ln(2(9.5)+1)+2ln(9.5-1) is ln(323.11182…)