What is 3log_{e}(2)+5log_{e}(pi)-log_{e}(9) ?

The solution to 3log_{e}(2)+5log_{e}(pi)-log_{e}(9) is ln((8pi^5)/9)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3log_{e}(2)+5log_{e}(pi)-log_{e}(9)

simplify

3 lo g_{e} (2) + 5 lo g_{e} (π) - lo g_{e} (9)

ln (\frac{8 π ^{5}}{9})

Decimal Notation

5.60586 \dots

Solution steps

3 lo g_{e} (2) + 5 lo g_{e} (π) - lo g_{e} (9)

Apply log rule:

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

3 lo g_{e} (2) = lo g_{e} (2^{3})

= lo g_{e} (2^{3}) + 5 lo g_{e} (π) - lo g_{e} (9)

Apply log rule:

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

5 lo g_{e} (π) = lo g_{e} (π^{5})

= lo g_{e} (2^{3}) + lo g_{e} (π^{5}) - lo g_{e} (9)

Apply log rule:

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

lo g_{e} (2^{3}) + lo g_{e} (π^{5}) = lo g_{e} (2^{3} π^{5})

= lo g_{e} (2^{3} π^{5}) - lo g_{e} (9)

2^{3} = 8

= lo g_{e} (8 π^{5}) - lo g_{e} (9)

Apply log rule:

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

lo g_{e} (8 π^{5}) - lo g_{e} (9) = lo g_{e} (\frac{8 π ^{5}}{9})

= lo g_{e} (\frac{8 π ^{5}}{9})

Apply log rule:

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

= ln (\frac{8 π ^{5}}{9})

lo g_{10} (A \cdot e^{- \frac{q}{r}})

ln (4) - 2 ln (8)

ln (\frac{1 ^{2} + 1}{2 ( 1 ) ^{2} + 1})

ln (\frac{400}{300})

- \frac{1}{9} ln (3)

What is 3log_{e}(2)+5log_{e}(pi)-log_{e}(9) ?
The solution to 3log_{e}(2)+5log_{e}(pi)-log_{e}(9) is ln((8pi^5)/9)