What is 1/2 log_{3}(x)-4log_{3}(y)-2log_{3}(z) ?

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

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)-4log_{3}(y)-2log_{3}(z)

simplify

\frac{1}{2} lo g_{3} (x) - 4 lo g_{3} (y) - 2 lo g_{3} (z)

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

Solution steps

\frac{1}{2} lo g_{3} (x) - 4 lo g_{3} (y) - 2 lo g_{3} (z)

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

- 4 lo g_{3} (y) = - lo g_{3} (y^{4})

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

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

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^{4}) = lo g_{3} (\frac{x ^{\frac{1}{2}}}{y ^{4}})

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

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

= lo g_{3} \frac{\frac{x ^{\frac{1}{2}}}{y ^{4}}}{z ^{2}}

Simplify

\frac{\frac{x ^{\frac{1}{2}}}{y ^{4}}}{z ^{2}} : \frac{x ^{\frac{1}{2}}}{y ^{4} z ^{2}}

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

Apply exponent rule:

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

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

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

ln (\frac{6}{5 x ^{5} y})

lo g_{10} (79 x y)

lo g_{4} (8) + lo g_{4} (15) - lo g_{4} (14)

- lo g_{10} (5.6 \cdot 1 0^{- 6})

lo g_{10} (\frac{y ^{4}}{x ^{5} z})

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