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Popular >

simplify 3ln(2)-ln(3)

Solution

simplify

3 ln (2) - ln (3)

Solution

ln (\frac{8}{3})

+1

Decimal Notation

0.98082 \dots

Solution steps

3 ln (2) - ln (3)

Apply log rule:

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

3 ln (2) = ln (2^{3})

= ln (2^{3}) - ln (3)

Apply log rule:

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

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

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

2^{3} = 8

= ln (\frac{8}{3})

Popular Examples

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14.77 + 10 \cdot lo g_{10} (\frac{179.68}{1.905})

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- lo g_{10} (7.2 \cdot 1 0^{- 6})

simplify 4.3279+log_{10}((0.47)/(0.29))simplify

4.3279 + lo g_{10} (\frac{0.47}{0.29})

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20 lo g_{10} (\frac{4 π}{299000})

simplify ln((n^2-n)/(n^2-n-2))simplify

ln (\frac{n ^{2} - n}{n ^{2} - n - 2})

Frequently Asked Questions (FAQ)

What is 3ln(2)-ln(3) ?
The solution to 3ln(2)-ln(3) is ln(8/3)