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Popular >

simplify ln(1/2)+ln(2/3)+ln(3/5)

Solution

simplify

ln (\frac{1}{2}) + ln (\frac{2}{3}) + ln (\frac{3}{5})

Solution

- ln (5)

+1

Decimal Notation

- 1.60943 \dots

Solution steps

ln (\frac{1}{2}) + ln (\frac{2}{3}) + ln (\frac{3}{5})

Apply log rule:

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

ln (\frac{1}{2}) + ln (\frac{2}{3}) = ln (\frac{1}{2} \cdot \frac{2}{3})

= ln (\frac{1}{2} \cdot \frac{2}{3}) + ln (\frac{3}{5})

Cross-cancel:

2

= ln (\frac{1}{3}) + ln (\frac{3}{5})

Apply log rule:

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

ln (\frac{1}{3}) + ln (\frac{3}{5}) = ln (\frac{1}{3} \cdot \frac{3}{5})

= ln (\frac{1}{3} \cdot \frac{3}{5})

Cross-cancel:

3

= ln (\frac{1}{5})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (5)

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Frequently Asked Questions (FAQ)

What is ln(1/2)+ln(2/3)+ln(3/5) ?
The solution to ln(1/2)+ln(2/3)+ln(3/5) is -ln(5)