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Popular >

simplify 8ln(8)-12ln(12)

Solution

simplify

8 ln (8) - 12 ln (12)

Solution

- 12 ln (3)

+1

Decimal Notation

- 13.18334 \dots

Solution steps

8 ln (8) - 12 ln (12)

Apply log rule:

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

8 ln (8) = ln (8^{8})

= ln (8^{8}) - 12 ln (12)

Apply log rule:

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

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

= ln (8^{8}) - ln (1 2^{12})

Apply log rule:

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

ln (8^{8}) - ln (1 2^{12}) = ln (\frac{8 ^{8}}{1 2 ^{12}})

= ln (\frac{8 ^{8}}{1 2 ^{12}})

\frac{8 ^{8}}{1 2 ^{12}} = \frac{1}{531441}

= ln (\frac{1}{531441})

Apply log rule:

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

= - ln (531441)

Rewrite

531441

in power-base form:

531441 = 3^{12}

= - ln (3^{12})

Apply log rule:

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

ln (3^{12}) = 12 ln (3)

= - 12 ln (3)

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Frequently Asked Questions (FAQ)

What is 8ln(8)-12ln(12) ?
The solution to 8ln(8)-12ln(12) is -12ln(3)