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Popular >

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

Solution

simplify

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

Solution

- 2 ln (3)

+1

Decimal Notation

- 2.19722 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{( - 1 ) ^{2}}{( - 3 ) ^{2}} = \frac{1}{9}

= ln (\frac{1}{9})

Apply log rule:

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

= - ln (9)

Rewrite

9

in power-base form:

9 = 3^{2}

= - ln (3^{2})

Apply log rule:

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

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

= - 2 ln (3)

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Frequently Asked Questions (FAQ)

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