What is ln(y^3)-ln(y)-ln(y^6) ?

The solution to ln(y^3)-ln(y)-ln(y^6) is -ln(y^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(y^3)-ln(y)-ln(y^6)

simplify

ln (y^{3}) - ln (y) - ln (y^{6})

- ln (y^{4})

Solution steps

ln (y^{3}) - ln (y) - ln (y^{6})

Apply log rule:

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

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

= ln (\frac{y ^{3}}{y}) - ln (y^{6})

Cancel the common factor:

y

= ln (y^{2}) - ln (y^{6})

Apply log rule:

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

ln (y^{2}) - ln (y^{6}) = ln (\frac{y ^{2}}{y ^{6}})

= ln (\frac{y ^{2}}{y ^{6}})

Simplify

\frac{y ^{2}}{y ^{6}} : \frac{1}{y ^{4}}

= ln (\frac{1}{y ^{4}})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (y^{4})

ln (\frac{8}{e ^{3}})

ln (0.5) + (ln (1.4)) + ln (84)

ln (- 2) - ln (1 + e^{- 2})

lo g_{10} (- 2 (1 + i))

ln (9 n) - 2 ln (3)

What is ln(y^3)-ln(y)-ln(y^6) ?
The solution to ln(y^3)-ln(y)-ln(y^6) is -ln(y^4)