What is log_{e}(9)+ln(8)-ln(10)-log_{e}(11) ?

The solution to log_{e}(9)+ln(8)-ln(10)-log_{e}(11) is ln(9/11)+ln(4/5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{e}(9)+ln(8)-ln(10)-log_{e}(11)

simplify

lo g_{e} (9) + ln (8) - ln (10) - lo g_{e} (11)

ln (\frac{9}{11}) + ln (\frac{4}{5})

Decimal Notation

- 0.42381 \dots

Solution steps

lo g_{e} (9) + ln (8) - ln (10) - lo g_{e} (11)

Apply log rule:

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

ln (8) - ln (10) = ln (\frac{8}{10})

= lo g_{e} (9) + ln (\frac{8}{10}) - lo g_{e} (11)

Cancel the common factor:

2

= lo g_{e} (9) + ln (\frac{4}{5}) - lo g_{e} (11)

Apply log rule:

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

lo g_{e} (9) - lo g_{e} (11) = lo g_{e} (\frac{9}{11})

= lo g_{e} (\frac{9}{11}) + ln (\frac{4}{5})

Apply log rule:

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

= ln (\frac{9}{11}) + ln (\frac{4}{5})

lo g_{3} (\frac{x}{2}) + lo g_{3} (16) - lo g_{3} (4)

lo g_{10} (\frac{x}{1000000})

lo g_{2} (3 a^{4})

10 lo g_{10} (5.2 x 1 0^{6})

What is log_{e}(9)+ln(8)-ln(10)-log_{e}(11) ?
The solution to log_{e}(9)+ln(8)-ln(10)-log_{e}(11) is ln(9/11)+ln(4/5)