What is 4ln(8)-2ln(920) ?

The solution to 4ln(8)-2ln(920) is ln(64/13225)

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simplify 4ln(8)-2ln(920)

simplify

4 ln (8) - 2 ln (920)

ln (\frac{64}{13225})

Decimal Notation

- 5.33098 \dots

Solution steps

4 ln (8) - 2 ln (920)

Apply log rule:

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

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

= ln (8^{4}) - 2 ln (920)

Apply log rule:

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

2 ln (920) = ln (92 0^{2})

= ln (8^{4}) - ln (92 0^{2})

Apply log rule:

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

ln (8^{4}) - ln (92 0^{2}) = ln (\frac{8 ^{4}}{92 0 ^{2}})

= ln (\frac{8 ^{4}}{92 0 ^{2}})

\frac{8 ^{4}}{92 0 ^{2}} = \frac{64}{13225}

= ln (\frac{64}{13225})

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