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Popular >

simplify ln(12)-ln(3)

Solution

simplify

ln (12) - ln (3)

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

ln (12) - ln (3)

Apply log rule:

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

ln (12) - ln (3) = ln (\frac{12}{3})

= ln (\frac{12}{3})

Divide the numbers:

\frac{12}{3} = 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)

Popular Examples

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lo g_{4} (\frac{64}{x + 3})

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lo g_{10} (16 x^{2}) + 2 lo g_{10} (\frac{1}{x})

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lo g_{10} (\frac{1}{x - 2})

Frequently Asked Questions (FAQ)

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