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Popular >

simplify 4*ln(-1)+ln(4)

Solution

simplify

4 \cdot ln (- 1) + ln (4)

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

4 ln (- 1) + ln (4)

Apply log rule:

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

4 ln (- 1) = ln ((- 1)^{4})

= ln ((- 1)^{4}) + ln (4)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((- 1)^{4}) + ln (4) = ln ((- 1)^{4} \cdot 4)

= ln ((- 1)^{4} \cdot 4)

(- 1)^{4} \cdot 4 = 4

= ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

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

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

= 2 ln (2)

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Frequently Asked Questions (FAQ)

What is 4*ln(-1)+ln(4) ?
The solution to 4*ln(-1)+ln(4) is 2ln(2)