en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2/3 ln(8)-2ln(4)+ln(24)

Solution

simplify

\frac{2}{3} ln (8) - 2 ln (4) + ln (24)

Solution

ln (6)

+1

Decimal Notation

1.79175 \dots

Solution steps

\frac{2}{3} ln (8) - 2 ln (4) + ln (24)

Apply log rule:

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

\frac{2}{3} ln (8) = ln (8^{\frac{2}{3}})

= ln (8^{\frac{2}{3}}) - 2 ln (4) + ln (24)

Apply log rule:

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

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

= ln (8^{\frac{2}{3}}) - ln (4^{2}) + ln (24)

Apply log rule:

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

ln (8^{\frac{2}{3}}) - ln (4^{2}) = ln (\frac{8 ^{\frac{2}{3}}}{4 ^{2}})

= ln (\frac{8 ^{\frac{2}{3}}}{4 ^{2}}) + ln (24)

\frac{8 ^{\frac{2}{3}}}{4 ^{2}} = \frac{1}{4}

= ln (\frac{1}{4}) + ln (24)

Apply log rule:

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

ln (\frac{1}{4}) + ln (24) = ln (24 \cdot \frac{1}{4})

= ln (24 \cdot \frac{1}{4})

\frac{1}{4} \cdot 24 = 6

= ln (6)

Popular Examples

simplify [ 1/2 (ln|x+1|-ln|x-1|)]simplify

[\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]

simplify log_{2}(10)+log_{2}(20)simplify

lo g_{2} (10) + lo g_{2} (20)

simplify log_{c}((a^2sqrt(c))/(b^3))simplify

lo g_{c} (\frac{a ^{2} c}{b ^{3}})

simplify 2log_{2}(x)-log_{2}(x+3)simplify

2 lo g_{2} (x) - lo g_{2} (x + 3)

simplify (3ln(7/4))/(ln(7)-2ln(2))-2 simplify

\frac{3 ln ( \frac{7}{4} )}{ln ( 7 ) - 2 ln ( 2 )} - 2

Frequently Asked Questions (FAQ)

What is 2/3 ln(8)-2ln(4)+ln(24) ?
The solution to 2/3 ln(8)-2ln(4)+ln(24) is ln(6)