What is ln(((1))/((2y)^3)) ?

The solution to ln(((1))/((2y)^3)) is -3ln(y)-3ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(((1))/((2y)^3))

simplify

ln (\frac{( 1 )}{( 2 y ) ^{3}})

- 3 ln (y) - 3 ln (2)

Solution steps

ln (\frac{( 1 )}{( 2 y ) ^{3}})

Apply log rule:

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

ln (\frac{( 1 )}{( 2 y ) ^{3}}) = ln ((1)) - ln ((2 y)^{3})

= ln (1) - ln ((2 y)^{3})

Apply log rule:

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

ln ((2 y)^{3}) = 3 ln (2 y)

= ln (1) - 3 ln (2 y)

Apply log rule:

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

3 ln (2 y) = 3 ln (2) + 3 ln (y)

= ln (1) - (3 ln (y) + 3 ln (2))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (3 ln (y) + 3 ln (2))

0 - (3 ln (2) + 3 ln (y)) = - (3 ln (2) + 3 ln (y))

= - (3 ln (y) + 3 ln (2))

Distribute parentheses

= - (3 ln (y)) - (3 ln (2))

Apply minus-plus rules

+ (- a) = - a

= - 3 ln (y) - 3 ln (2)

ln (A \cdot e^{B x})

- lo g_{10} (3.2 x 1 0^{- 4})

ln (x x^{2} - 9)

6 [ln (x) - ln (x + 7) - ln (x - 7)]

lo g_{π} (2 π)

What is ln(((1))/((2y)^3)) ?
The solution to ln(((1))/((2y)^3)) is -3ln(y)-3ln(2)