What is 3ln(x)-4ln(y)-5ln(z) ?

The solution to 3ln(x)-4ln(y)-5ln(z) is ln((x^3)/(y^4z^5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3ln(x)-4ln(y)-5ln(z)

simplify

3 ln (x) - 4 ln (y) - 5 ln (z)

ln (\frac{x ^{3}}{y ^{4} z ^{5}})

Solution steps

3 ln (x) - 4 ln (y) - 5 ln (z)

Apply log rule:

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

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

= ln (x^{3}) - 4 ln (y) - 5 ln (z)

Apply log rule:

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

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

= ln (x^{3}) - ln (y^{4}) - 5 ln (z)

Apply log rule:

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

ln (x^{3}) - ln (y^{4}) = ln (\frac{x ^{3}}{y ^{4}})

= ln (\frac{x ^{3}}{y ^{4}}) - 5 ln (z)

Apply log rule:

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

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

= ln (\frac{x ^{3}}{y ^{4}}) - ln (z^{5})

Apply log rule:

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

ln (\frac{x ^{3}}{y ^{4}}) - ln (z^{5}) = ln (\frac{\frac{x ^{3}}{y ^{4}}}{z ^{5}})

= ln (\frac{\frac{x ^{3}}{y ^{4}}}{z ^{5}})

Apply the fraction rule:

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

= ln (\frac{x ^{3}}{y ^{4} z ^{5}})

- lo g_{10} (5 \times 1 0^{- 5})

5 lo g_{b} (x) + 3 lo g_{b} (z)

- 0.45 lo g_{2} (0.45) - 0.55 lo g_{2} (0.55)

lo g_{4} (2 x^{2})

lo g_{10} (\frac{5}{x + 1})

What is 3ln(x)-4ln(y)-5ln(z) ?
The solution to 3ln(x)-4ln(y)-5ln(z) is ln((x^3)/(y^4z^5))