What is simplify-ln(x)+9ln(y)-3ln(z) ?

The solution to simplify-ln(x)+9ln(y)-3ln(z) is ln((y^9)/(xz^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-ln(x)+9ln(y)-3ln(z)

simplify

- ln (x) + 9 ln (y) - 3 ln (z)

ln (\frac{y ^{9}}{x z ^{3}})

Solution steps

- ln (x) + 9 ln (y) - 3 ln (z)

Apply log rule:

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

9 ln (y) = ln (y^{9})

= - ln (x) + ln (y^{9}) - 3 ln (z)

Apply log rule:

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

ln (y^{9}) - ln (x) = ln (\frac{y ^{9}}{x})

= ln (\frac{y ^{9}}{x}) - 3 ln (z)

Apply log rule:

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

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

= ln (\frac{y ^{9}}{x}) - ln (z^{3})

Apply log rule:

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

ln (\frac{y ^{9}}{x}) - ln (z^{3}) = ln (\frac{\frac{y ^{9}}{x}}{z ^{3}})

= ln (\frac{\frac{y ^{9}}{x}}{z ^{3}})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{y ^{9}}{x z ^{3}})

ln (\frac{n + 1}{n - 1})

ln (\frac{x}{e ^{x} ( x + 3 ) ^{2}})

ln (\frac{x ^{9} x ^{2} + 2}{( x + 2 ) ^{5}})

\frac{2.3 \cdot 9 \cdot 12}{150 \cdot 10800} \cdot ln (\frac{70}{30})

- ln (\frac{V}{N x}) - ln (\frac{bV}{N x})

What is simplify-ln(x)+9ln(y)-3ln(z) ?
The solution to simplify-ln(x)+9ln(y)-3ln(z) is ln((y^9)/(xz^3))