en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(6)+1ln(4)-ln(3)

Solution

simplify

ln (6) + 1 ln (4) - ln (3)

Solution

3 ln (2)

+1

Decimal Notation

2.07944 \dots

Solution steps

ln (6) + 1 \cdot ln (4) - ln (3)

Apply log rule:

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

1 \cdot ln (4) = ln (4^{1})

= ln (6) + ln (4^{1}) - ln (3)

Apply log rule:

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

ln (6) + ln (4^{1}) = ln (6 \cdot 4^{1})

= ln (6 \cdot 4^{1}) - ln (3)

6 \cdot 4^{1} = 24

= ln (24) - ln (3)

Apply log rule:

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

ln (24) - ln (3) = ln (\frac{24}{3})

= ln (\frac{24}{3})

Divide the numbers:

\frac{24}{3} = 8

= ln (8)

Rewrite

8

in power-base form:

8 = 2^{3}

= ln (2^{3})

Apply log rule:

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

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

= 3 ln (2)

Popular Examples

simplify ln((2.46)/(17.39))simplify

ln (\frac{2.46}{17.39})

simplify ln((6.5)/(3.3))simplify

ln (\frac{6.5}{3.3})

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

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

join 3/2 ln(4+sqrt(19))join

\frac{3}{2} ln (4 + 19)

simplify 1/2 ln(3.73)-ln(0.26)simplify

\frac{1}{2} ln (3.73) - ln (0.26)

Frequently Asked Questions (FAQ)

What is ln(6)+1ln(4)-ln(3) ?
The solution to ln(6)+1ln(4)-ln(3) is 3ln(2)