What is ln(8)-ln(2)-ln(1/4) ?

The solution to ln(8)-ln(2)-ln(1/4) is 4ln(2)

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simplify ln(8)-ln(2)-ln(1/4)

simplify

ln (8) - ln (2) - ln (\frac{1}{4})

4 ln (2)

Decimal Notation

2.77258 \dots

Solution steps

ln (8) - ln (2) - ln (\frac{1}{4})

Rewrite

- ln (2) - ln (\frac{1}{4})

- (ln (2) + ln (\frac{1}{4}))

= ln (8) - (ln (2) + ln (\frac{1}{4}))

Apply log rule:

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

ln (2) + ln (\frac{1}{4}) = ln (2 \cdot \frac{1}{4})

= ln (8) - ln (2 \cdot \frac{1}{4})

2 \cdot \frac{1}{4} = \frac{1}{2}

= ln (8) - ln (\frac{1}{2})

ln (8) = 3 ln (2)

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

= 3 ln (2) - (- ln (2))

Apply rule

- (- a) = a

= 3 ln (2) + ln (2)

Add similar elements:

3 ln (2) + ln (2) = 4 ln (2)

= 4 ln (2)

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