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Popular >

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

Solution

simplify

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

Solution

- 2 ln (2)

+1

Decimal Notation

- 1.38629 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{\frac{1}{8}}{\frac{1}{2}} = \frac{1}{4}

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

Apply log rule:

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

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