en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(6)-ln(4)

Solution

simplify

2 ln (6) - ln (4)

Solution

2 ln (3)

+1

Decimal Notation

2.19722 \dots

Solution steps

2 ln (6) - ln (4)

Apply log rule:

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

2 ln (6) = ln (6^{2})

= ln (6^{2}) - ln (4)

Apply log rule:

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

ln (6^{2}) - ln (4) = ln (\frac{6 ^{2}}{4})

= ln (\frac{6 ^{2}}{4})

\frac{6 ^{2}}{4} = 9

= ln (9)

Rewrite

9

in power-base form:

9 = 3^{2}

= ln (3^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (3^{2}) = 2 ln (3)

= 2 ln (3)

Popular Examples

simplify ln(x^2*y)simplify

ln (x^{2} \cdot y)

simplify 5ln(x^{1/2})+ln(9x)simplify

5 ln (x^{\frac{1}{2}}) + ln (9 x)

simplify ln(x/(y^2))simplify

ln (\frac{x}{y ^{2}})

simplify a+ln(bx)simplify

a + ln (b x)

simplify ln(xy^2z^3)simplify

ln (x y^{2} z^{3})

Frequently Asked Questions (FAQ)

What is 2ln(6)-ln(4) ?
The solution to 2ln(6)-ln(4) is 2ln(3)