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Popular >

simplify ln(8)-2ln(4)

Solution

simplify

ln (8) - 2 ln (4)

Solution

- ln (2)

+1

Decimal Notation

- 0.69314 \dots

Solution steps

ln (8) - 2 ln (4)

Apply log rule:

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

2 ln (4) = ln (4^{2})

= ln (8) - ln (4^{2})

Apply log rule:

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

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

= ln (\frac{8}{4 ^{2}})

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

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

Apply log rule:

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

= - ln (2)

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Frequently Asked Questions (FAQ)

What is ln(8)-2ln(4) ?
The solution to ln(8)-2ln(4) is -ln(2)