What is log_{e}(((2*9+12))/9)-((9+12))/(2*9+12) ?

The solution to log_{e}(((2*9+12))/9)-((9+12))/(2*9+12) is ln(30)-2ln(3)-7/10

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{e}(((29+12))/9)-((9+12))/(29+12)

simplify

lo g_{e} (\frac{( 2 \cdot 9 + 12 )}{9}) - \frac{( 9 + 12 )}{2 \cdot 9 + 12}

ln (30) - 2 ln (3) - \frac{7}{10}

Decimal Notation

0.50397 \dots

Solution steps

lo g_{e} (\frac{( 2 \cdot 9 + 12 )}{9}) - \frac{( 9 + 12 )}{2 \cdot 9 + 12}

Apply log rule:

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

lo g_{e} (\frac{( 2 \cdot 9 + 12 )}{9}) = lo g_{e} ((2 \cdot 9 + 12)) - lo g_{e} (9)

= lo g_{e} (2 \cdot 9 + 12) - lo g_{e} (9) - \frac{9 + 12}{2 \cdot 9 + 12}

lo g_{e} (2 \cdot 9 + 12) = ln (30)

lo g_{e} (9) = ln (9)

\frac{9 + 12}{2 \cdot 9 + 12} = \frac{7}{10}

= ln (30) - ln (9) - \frac{7}{10}

ln (9) = 2 ln (3)

= ln (30) - 2 ln (3) - \frac{7}{10}

ln (16 \frac{1}{3})

ln (\frac{129}{122})

- lo g_{10} (7.3 \cdot 1 0^{- 11})

ln (\frac{e ^{9}}{x y ^{8}})

\frac{14}{3} ln (\frac{9}{8}) - \frac{11}{3} ln (2)

What is log_{e}(((2*9+12))/9)-((9+12))/(2*9+12) ?
The solution to log_{e}(((2*9+12))/9)-((9+12))/(2*9+12) is ln(30)-2ln(3)-7/10