What is simplify-1/6 ln(12)+1/6 ln(6) ?

The solution to simplify-1/6 ln(12)+1/6 ln(6) is -1/6 ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-1/6 ln(12)+1/6 ln(6)

simplify

- \frac{1}{6} ln (12) + \frac{1}{6} ln (6)

- \frac{1}{6} ln (2)

Decimal Notation

- 0.11552 \dots

Solution steps

- \frac{1}{6} ln (12) + \frac{1}{6} ln (6)

Apply log rule:

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

\frac{1}{6} ln (12) = ln (1 2^{\frac{1}{6}})

= - ln (1 2^{\frac{1}{6}}) + \frac{1}{6} ln (6)

Apply log rule:

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

\frac{1}{6} ln (6) = ln (6^{\frac{1}{6}})

= - ln (1 2^{\frac{1}{6}}) + ln (6^{\frac{1}{6}})

Apply log rule:

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

ln (6^{\frac{1}{6}}) - ln (1 2^{\frac{1}{6}}) = ln (\frac{6 ^{\frac{1}{6}}}{1 2 ^{\frac{1}{6}}})

= ln (\frac{6 ^{\frac{1}{6}}}{1 2 ^{\frac{1}{6}}})

Rewrite as

= ln ((\frac{1}{2})^{\frac{1}{6}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{6} ln (\frac{1}{2})

Simplify

ln (\frac{1}{2}) : - ln (2)

= \frac{1}{6} (- ln (2))

Remove parentheses:

(- a) = - a

= - \frac{1}{6} ln (2)

\frac{1}{2} ln (3 e^{2 x})

ln (\frac{e ^{3 x} x}{sin ( 7 x )})

ln (\frac{3 + 1}{3})

4 lo g_{10} (x) - 3 lo g_{10} (y)

\frac{1}{8} (ln (6) - 2 ln (2))

What is simplify-1/6 ln(12)+1/6 ln(6) ?
The solution to simplify-1/6 ln(12)+1/6 ln(6) is -1/6 ln(2)