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Popular >

simplify 3ln(-1)-3ln(-2)

Solution

simplify

3 ln (- 1) - 3 ln (- 2)

Solution

- 3 ln (2)

+1

Decimal Notation

- 2.07944 \dots

Solution steps

3 ln (- 1) - 3 ln (- 2)

Apply log rule:

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

3 ln (- 1) = ln ((- 1)^{3})

= ln ((- 1)^{3}) - 3 ln (- 2)

Apply log rule:

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

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

= ln ((- 1)^{3}) - ln ((- 2)^{3})

Apply log rule:

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

ln ((- 1)^{3}) - ln ((- 2)^{3}) = ln (\frac{( - 1 ) ^{3}}{( - 2 ) ^{3}})

= ln (\frac{( - 1 ) ^{3}}{( - 2 ) ^{3}})

\frac{( - 1 ) ^{3}}{( - 2 ) ^{3}} = \frac{1}{8}

= ln (\frac{1}{8})

Apply log rule:

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

= - ln (8)

Rewrite

8

in power-base form:

8 = 2^{3}

= - ln (2^{3})

Apply log rule:

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

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

= - 3 ln (2)

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Frequently Asked Questions (FAQ)

What is 3ln(-1)-3ln(-2) ?
The solution to 3ln(-1)-3ln(-2) is -3ln(2)