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Popular >

simplify 2ln(3)-4ln(6)

Solution

simplify

2 ln (3) - 4 ln (6)

Solution

- 2 ln (12)

+1

Decimal Notation

- 4.96981 \dots

Solution steps

2 ln (3) - 4 ln (6)

Apply log rule:

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

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

= ln (3^{2}) - 4 ln (6)

Apply log rule:

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

4 ln (6) = ln (6^{4})

= ln (3^{2}) - ln (6^{4})

Apply log rule:

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

ln (3^{2}) - ln (6^{4}) = ln (\frac{3 ^{2}}{6 ^{4}})

= ln (\frac{3 ^{2}}{6 ^{4}})

\frac{3 ^{2}}{6 ^{4}} = \frac{1}{144}

= ln (\frac{1}{144})

Apply log rule:

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

= - ln (144)

Rewrite

144

in power-base form:

144 = 1 2^{2}

= - ln (1 2^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 2^{2}) = 2 ln (12)

= - 2 ln (12)

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Frequently Asked Questions (FAQ)

What is 2ln(3)-4ln(6) ?
The solution to 2ln(3)-4ln(6) is -2ln(12)