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Popular >

simplify ln(2)-2ln(6)

Solution

simplify

ln (2) - 2 ln (6)

Solution

- ln (18)

+1

Decimal

- 2.89037 \dots

Solution steps

ln (2) - 2 ln (6)

Apply log rule:

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

2 ln (6) = ln (6^{2})

= ln (2) - ln (6^{2})

Apply log rule:

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

ln (2) - ln (6^{2}) = ln (\frac{2}{6 ^{2}})

= ln (\frac{2}{6 ^{2}})

\frac{2}{6 ^{2}} = \frac{1}{18}

= ln (\frac{1}{18})

Apply log rule:

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

= - ln (18)

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Frequently Asked Questions (FAQ)

What is ln(2)-2ln(6) ?
The solution to ln(2)-2ln(6) is -ln(18)