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Popular >

simplify 2ln(5)-2ln(2)

Solution

simplify

2 ln (5) - 2 ln (2)

Solution

ln (\frac{25}{4})

+1

Decimal Notation

1.83258 \dots

Solution steps

2 ln (5) - 2 ln (2)

Apply log rule:

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

2 ln (5) = ln (5^{2})

= ln (5^{2}) - 2 ln (2)

Apply log rule:

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

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

= ln (5^{2}) - ln (2^{2})

Apply log rule:

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

ln (5^{2}) - ln (2^{2}) = ln (\frac{5 ^{2}}{2 ^{2}})

= ln (\frac{5 ^{2}}{2 ^{2}})

\frac{5 ^{2}}{2 ^{2}} = \frac{25}{4}

= ln (\frac{25}{4})

Popular Examples

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\frac{21}{2} + ln (\frac{2}{5})

simplify-log_{10}(5.916*10^{-5})simplify

- lo g_{10} (5.916 \cdot 1 0^{- 5})

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ln (- e^{- x} \cdot x^{k})

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lo g_{2} (\frac{1}{40})

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- lo g_{10} (7.94 \cdot 1 0^{- 5})

Frequently Asked Questions (FAQ)

What is 2ln(5)-2ln(2) ?
The solution to 2ln(5)-2ln(2) is ln(25/4)