What is ln(((2^2))/(3^45^3)) ?

The solution to ln(((2^2))/(3^45^3)) is 2ln(2)-4ln(3)-3ln(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(((2^2))/(3^45^3))

simplify

ln (\frac{( 2 ^{2} )}{3 ^{4} 5 ^{3}})

2 ln (2) - 4 ln (3) - 3 ln (5)

Decimal Notation

- 7.83646 \dots

Solution steps

ln (\frac{( 2 ^{2} )}{3 ^{4} \cdot 5 ^{3}})

Apply log rule:

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

ln (\frac{( 2 ^{2} )}{3 ^{4} \cdot 5 ^{3}}) = ln ((2^{2})) - ln (3^{4} \cdot 5^{3})

= ln (2^{2}) - ln (3^{4} \cdot 5^{3})

Apply log rule:

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

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

= 2 ln (2) - ln (3^{4} \cdot 5^{3})

Apply log rule:

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

ln (3^{4} \cdot 5^{3}) = ln (3^{4}) + ln (5^{3})

= 2 ln (2) - (ln (3^{4}) + ln (5^{3}))

Apply log rule:

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

ln (3^{4}) = 4 ln (3)

= 2 ln (2) - (4 ln (3) + ln (5^{3}))

Apply log rule:

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

ln (5^{3}) = 3 ln (5)

= 2 ln (2) - (4 ln (3) + 3 ln (5))

- (4 ln (3) + 3 ln (5)) : - 4 ln (3) - 3 ln (5)

= 2 ln (2) - 4 ln (3) - 3 ln (5)

- ln (2 - 1) + ln (2 + 1)

ln (0.5 t e^{- 0.5 t})

6 lo g_{e} (x) + 4 lo g_{e} (y)

ln (5 x)

- lo g_{0.5} (2 x) - 3

What is ln(((2^2))/(3^45^3)) ?
The solution to ln(((2^2))/(3^45^3)) is 2ln(2)-4ln(3)-3ln(5)