What is 1/2 log_{3}(x)-2log_{3}(y)-log_{3}(z) ?

The solution to 1/2 log_{3}(x)-2log_{3}(y)-log_{3}(z) is log_{3}((sqrt(x))/(y^2z))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 log_{3}(x)-2log_{3}(y)-log_{3}(z)

simplify

\frac{1}{2} lo g_{3} (x) - 2 lo g_{3} (y) - lo g_{3} (z)

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

Solution steps

\frac{1}{2} lo g_{3} (x) - 2 lo g_{3} (y) - lo g_{3} (z)

\frac{1}{2} lo g_{3} (x) = lo g_{3} (x^{\frac{1}{2}})

- 2 lo g_{3} (y) = - lo g_{3} (y^{2})

= lo g_{3} (x^{\frac{1}{2}}) - lo g_{3} (y^{2}) - lo g_{3} (z)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{3} (x^{\frac{1}{2}}) - lo g_{3} (y^{2}) = lo g_{3} (\frac{x ^{\frac{1}{2}}}{y ^{2}})

= lo g_{3} (\frac{x ^{\frac{1}{2}}}{y ^{2}}) - lo g_{3} (z)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{3} (\frac{x ^{\frac{1}{2}}}{y ^{2}}) - lo g_{3} (z) = lo g_{3} \frac{\frac{x ^{\frac{1}{2}}}{y ^{2}}}{z}

= lo g_{3} \frac{\frac{x ^{\frac{1}{2}}}{y ^{2}}}{z}

Simplify

\frac{\frac{x ^{\frac{1}{2}}}{y ^{2}}}{z} : \frac{x ^{\frac{1}{2}}}{y ^{2} z}

= lo g_{3} (\frac{x ^{\frac{1}{2}}}{y ^{2} z})

Apply exponent rule:

a^{\frac{1}{2}} = a

x^{\frac{1}{2}} = x

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

ln (5 e^{2})

lo g_{10} (z^{5} x^{3} y)

lo g_{10} (\frac{p q ^{3}}{s})

lo g_{10} (\frac{c ^{6}}{a b ^{3}})

lo g_{b} (4) + lo g_{b} (3)

What is 1/2 log_{3}(x)-2log_{3}(y)-log_{3}(z) ?
The solution to 1/2 log_{3}(x)-2log_{3}(y)-log_{3}(z) is log_{3}((sqrt(x))/(y^2z))