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Popular >

simplify 2ln(3)-ln(18)

Solution

simplify

2 ln (3) - ln (18)

Solution

- ln (2)

+1

Decimal Notation

- 0.69314 \dots

Solution steps

2 ln (3) - ln (18)

Apply log rule:

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

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

= ln (3^{2}) - ln (18)

Apply log rule:

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

ln (3^{2}) - ln (18) = ln (\frac{3 ^{2}}{18})

= ln (\frac{3 ^{2}}{18})

\frac{3 ^{2}}{18} = \frac{1}{2}

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

Apply log rule:

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

= - ln (2)

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Frequently Asked Questions (FAQ)

What is 2ln(3)-ln(18) ?
The solution to 2ln(3)-ln(18) is -ln(2)