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Popular >

simplify 2ln|2|-2ln| 1/4 |

Solution

simplify

2 ln ∣ 2 ∣ - 2 ln \frac{1}{4}

Solution

6 ln (2)

+1

Decimal Notation

4.15888 \dots

Solution steps

2 ln ∣ 2 ∣ - 2 ln \frac{1}{4}

Apply log rule:

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

2 ln ∣ 2 ∣ = ln (∣ 2 ∣^{2})

= ln (∣ 2 ∣^{2}) - 2 ln \frac{1}{4}

Apply log rule:

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

2 ln \frac{1}{4} = ln (\frac{1}{4}^{2})

= ln (∣ 2 ∣^{2}) - ln (\frac{1}{4}^{2})

Apply log rule:

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

ln (∣ 2 ∣^{2}) - ln (\frac{1}{4}^{2}) = ln (\frac{∣ 2 ∣ ^{2}}{\frac{1}{4} ^{2}})

= ln (\frac{∣ 2 ∣ ^{2}}{\frac{1}{4} ^{2}})

\frac{∣ 2 ∣ ^{2}}{\frac{1}{4} ^{2}} = 64

= ln (64)

Rewrite

64

in power-base form:

64 = 2^{6}

= ln (2^{6})

Apply log rule:

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

ln (2^{6}) = 6 ln (2)

= 6 ln (2)

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Frequently Asked Questions (FAQ)

What is 2ln|2|-2ln| 1/4 | ?
The solution to 2ln|2|-2ln| 1/4 | is 6ln(2)