en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(8)-2ln(6)+ln(18)

Solution

simplify

ln (8) - 2 ln (6) + ln (18)

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

ln (8) - 2 ln (6) + ln (18)

Apply log rule:

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

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

= ln (8) - ln (6^{2}) + ln (18)

Apply log rule:

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

ln (8) - ln (6^{2}) = ln (\frac{8}{6 ^{2}})

= ln (\frac{8}{6 ^{2}}) + ln (18)

\frac{8}{6 ^{2}} = \frac{2}{9}

= ln (\frac{2}{9}) + ln (18)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{2}{9}) + ln (18) = ln (18 \cdot \frac{2}{9})

= ln (18 \cdot \frac{2}{9})

\frac{2}{9} \cdot 18 = 4

= ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

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

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

= 2 ln (2)

Popular Examples

simplify log_{7}(3x^2)-e^{3x-6}simplify

lo g_{7} (3 x^{2}) - e^{3 x - 6}

simplify ln(λ/(2pi))simplify

ln (\frac{λ}{2 π})

simplify ln(1922000/2853)simplify

ln (\frac{1922000}{2853})

simplify 1/30 ln(15/22)simplify

\frac{1}{30} ln (\frac{15}{22})

simplify log_{b}(0.78)-log_{b}(0.82)simplify

lo g_{b} (0.78) - lo g_{b} (0.82)

Frequently Asked Questions (FAQ)

What is ln(8)-2ln(6)+ln(18) ?
The solution to ln(8)-2ln(6)+ln(18) is 2ln(2)