What is 1/2 ln(x)+4ln(y)-3ln(z) ?

The solution to 1/2 ln(x)+4ln(y)-3ln(z) is ln((x^{1/2}y^4)/(z^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 ln(x)+4ln(y)-3ln(z)

simplify

\frac{1}{2} ln (x) + 4 ln (y) - 3 ln (z)

ln (\frac{x ^{\frac{1}{2}} y ^{4}}{z ^{3}})

Solution steps

\frac{1}{2} ln (x) + 4 ln (y) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{\frac{1}{2}}) + 4 ln (y) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{\frac{1}{2}}) + ln (y^{4}) - 3 ln (z)

Apply log rule:

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

ln (x^{\frac{1}{2}}) + ln (y^{4}) = ln (y^{4} x^{\frac{1}{2}})

= ln (x^{\frac{1}{2}} y^{4}) - 3 ln (z)

Apply log rule:

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

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

= ln (y^{4} x^{\frac{1}{2}}) - ln (z^{3})

Apply log rule:

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

ln (y^{4} x^{\frac{1}{2}}) - ln (z^{3}) = ln (\frac{y ^{4} x ^{\frac{1}{2}}}{z ^{3}})

= ln (\frac{x ^{\frac{1}{2}} y ^{4}}{z ^{3}})

lo g_{9} (x^{2} + 13 x + 40) - lo g_{9} (x + 8)

3.8 + lo g_{10} (\frac{0.2 - 0.02}{0.5 + 0.02})

lo g_{2} (\frac{8 a ^{2} 2 - b}{c ( b + 3 ) ^{2}})

lo g_{10} (\frac{x ^{2} y ^{3}}{z ^{4}})

lo g_{2} (\frac{z}{8})

What is 1/2 ln(x)+4ln(y)-3ln(z) ?
The solution to 1/2 ln(x)+4ln(y)-3ln(z) is ln((x^{1/2}y^4)/(z^3))