en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

simplify

2 ln (5) - 2 ln (2)

Solution

ln (\frac{25}{4})

+1

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

simplify 21/2+ln(2/5)simplify

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

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

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

simplify ln(-e^{-x}*x^k)simplify

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

simplify log_{2}(1/40)simplify

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

simplify-log_{10}(7.94*10^{-5})simplify

- 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)