What is ln(x/(y^3sqrt(z))) ?

The solution to ln(x/(y^3sqrt(z))) is ln(x)-3ln(y)-ln(sqrt(z))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x/(y^3sqrt(z)))

simplify

ln (\frac{x}{y ^{3} z})

ln (x) - 3 ln (y) - ln (z)

Solution steps

ln (\frac{x}{y ^{3} z})

Apply log rule:

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

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

= ln (x) - ln (y^{3} z)

Apply log rule:

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

ln (y^{3} z) = ln (y^{3}) + ln (z)

= ln (x) - (ln (y^{3}) + ln (z))

Apply log rule:

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

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

= ln (x) - (3 ln (y) + ln (z))

- (3 ln (y) + ln (z)) : - 3 ln (y) - ln (z)

= ln (x) - 3 ln (y) - ln (z)

- lo g_{10} (4.95 \cdot 1 0^{- 6})

ln (10) - ln (25)

22.2 \cdot ln (\frac{273}{263})

ln (1000 e^{an + b})

ln (\frac{0.5}{1.25})

What is ln(x/(y^3sqrt(z))) ?
The solution to ln(x/(y^3sqrt(z))) is ln(x)-3ln(y)-ln(sqrt(z))