en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4ln(3)-2ln(5)

Solution

simplify

4 ln (3) - 2 ln (5)

Solution

ln (\frac{81}{25})

+1

Decimal Notation

1.17557 \dots

Solution steps

4 ln (3) - 2 ln (5)

Apply log rule:

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

4 ln (3) = ln (3^{4})

= ln (3^{4}) - 2 ln (5)

Apply log rule:

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

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

= ln (3^{4}) - ln (5^{2})

Apply log rule:

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

ln (3^{4}) - ln (5^{2}) = ln (\frac{3 ^{4}}{5 ^{2}})

= ln (\frac{3 ^{4}}{5 ^{2}})

\frac{3 ^{4}}{5 ^{2}} = \frac{81}{25}

= ln (\frac{81}{25})

Popular Examples

simplify ln(15)+ln(3)simplify

ln (15) + ln (3)

simplify 4ln(3)-2ln(2)simplify

4 ln (3) - 2 ln (2)

simplify-ln(2)-ln(2/3)simplify

- ln (2) - ln (\frac{2}{3})

simplify ln((cos(2x))/(cos(x)))simplify

ln (\frac{cos ( 2 x )}{cos ( x )})

simplify 3ln(x)+1/2 ln(y)-8 simplify

3 ln (x) + \frac{1}{2} ln (y) - 8

Frequently Asked Questions (FAQ)

What is 4ln(3)-2ln(5) ?
The solution to 4ln(3)-2ln(5) is ln(81/25)