What is 5ln(x)+1/2 ln(y)-7ln(z) ?

The solution to 5ln(x)+1/2 ln(y)-7ln(z) is ln((x^5y^{1/2})/(z^7))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 5ln(x)+1/2 ln(y)-7ln(z)

simplify

5 ln (x) + \frac{1}{2} ln (y) - 7 ln (z)

ln (\frac{x ^{5} y ^{\frac{1}{2}}}{z ^{7}})

Solution steps

5 ln (x) + \frac{1}{2} ln (y) - 7 ln (z)

Apply log rule:

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

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

= ln (x^{5}) + \frac{1}{2} ln (y) - 7 ln (z)

Apply log rule:

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

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

= ln (x^{5}) + ln (y^{\frac{1}{2}}) - 7 ln (z)

Apply log rule:

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

ln (x^{5}) + ln (y^{\frac{1}{2}}) = ln (x^{5} y^{\frac{1}{2}})

= ln (x^{5} y^{\frac{1}{2}}) - 7 ln (z)

Apply log rule:

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

7 ln (z) = ln (z^{7})

= ln (x^{5} y^{\frac{1}{2}}) - ln (z^{7})

Apply log rule:

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

ln (x^{5} y^{\frac{1}{2}}) - ln (z^{7}) = ln (\frac{x ^{5} y ^{\frac{1}{2}}}{z ^{7}})

= ln (\frac{x ^{5} y ^{\frac{1}{2}}}{z ^{7}})

lo g_{10} (4) + lo g_{10} (3) - lo g_{10} (2)

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

- lo g_{10} (2 \cdot 1 0^{- 3})

ln (x) + ln (x - 10)

- lo g_{10} (2 \cdot 1 0^{- 5})

What is 5ln(x)+1/2 ln(y)-7ln(z) ?
The solution to 5ln(x)+1/2 ln(y)-7ln(z) is ln((x^5y^{1/2})/(z^7))