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Popular >

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

Solution

simplify

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

Solution

5 - ln (6)

+1

Decimal Notation

3.20824 \dots

Solution steps

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

Apply log rule:

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

ln (\frac{1}{3}) - ln (2) = ln (\frac{\frac{1}{3}}{2})

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

\frac{\frac{1}{3}}{2} = \frac{1}{6}

= 5 + ln (\frac{1}{6})

Apply log rule:

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

= 5 - ln (6)

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Frequently Asked Questions (FAQ)

What is 5-ln(2)+ln(1/3) ?
The solution to 5-ln(2)+ln(1/3) is 5-ln(6)