What is 13ln(208/3)+7ln(80-0.75*208/3) ?

The solution to 13ln(208/3)+7ln(80-0.75*208/3) is 13(ln(208)-ln(3))+7ln(28)

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simplify 13ln(208/3)+7ln(80-0.75*208/3)

simplify

13 ln (\frac{208}{3}) + 7 ln (80 - 0.75 \cdot \frac{208}{3})

13 (ln (208) - ln (3)) + 7 ln (28)

Decimal Notation

78.43146 \dots

Solution steps

13 ln (\frac{208}{3}) + 7 ln (80 - 0.75 \cdot \frac{208}{3})

Apply log rule:

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

ln (\frac{208}{3}) = ln (208) - ln (3)

= 13 (ln (208) - ln (3)) + 7 ln (- 0.75 \cdot \frac{208}{3} + 80)

7 ln (80 - 0.75 \cdot \frac{208}{3}) = 7 ln (28)

= 13 (ln (208) - ln (3)) + 7 ln (28)

ln (\frac{41}{10}) - \frac{1}{4}

\frac{1}{4} ln (x + 2) - \frac{1}{4} ln (x - 2)

ln (\frac{273.15}{262.05})

ln (2) + 5 ln (x - 1) - 2 ln (x + 3)

2 ln (x - 4) - ln (x + 4) - ln (x^{2} - 16) + ln (4) + ln (x)

What is 13ln(208/3)+7ln(80-0.75*208/3) ?
The solution to 13ln(208/3)+7ln(80-0.75*208/3) is 13(ln(208)-ln(3))+7ln(28)