What is 3log_{6}(x)+2log_{6}(y)-1/2 log_{6}(z) ?

The solution to 3log_{6}(x)+2log_{6}(y)-1/2 log_{6}(z) is log_{6}((x^3y^2sqrt(z))/z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3log_{6}(x)+2log_{6}(y)-1/2 log_{6}(z)

simplify

3 lo g_{6} (x) + 2 lo g_{6} (y) - \frac{1}{2} lo g_{6} (z)

lo g_{6} (\frac{x ^{3} y ^{2} z}{z})

Solution steps

3 lo g_{6} (x) + 2 lo g_{6} (y) - \frac{1}{2} lo g_{6} (z)

Apply log rule:

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

3 lo g_{6} (x) = lo g_{6} (x^{3})

= lo g_{6} (x^{3}) + 2 lo g_{6} (y) - \frac{1}{2} lo g_{6} (z)

Apply log rule:

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

2 lo g_{6} (y) = lo g_{6} (y^{2})

= lo g_{6} (x^{3}) + lo g_{6} (y^{2}) - \frac{1}{2} lo g_{6} (z)

Apply log rule:

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

lo g_{6} (x^{3}) + lo g_{6} (y^{2}) = lo g_{6} (x^{3} y^{2})

= lo g_{6} (x^{3} y^{2}) - \frac{1}{2} lo g_{6} (z)

Apply log rule:

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

\frac{1}{2} lo g_{6} (z) = lo g_{6} (z^{\frac{1}{2}})

= lo g_{6} (x^{3} y^{2}) - lo g_{6} (z^{\frac{1}{2}})

Apply log rule:

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

lo g_{6} (x^{3} y^{2}) - lo g_{6} (z^{\frac{1}{2}}) = lo g_{6} (\frac{x ^{3} y ^{2}}{z ^{\frac{1}{2}}})

= lo g_{6} (\frac{x ^{3} y ^{2}}{z ^{\frac{1}{2}}})

Simplify

\frac{x ^{3} y ^{2}}{z ^{\frac{1}{2}}} : \frac{x ^{3} y ^{2} z}{z}

= lo g_{6} (\frac{x ^{3} y ^{2} z}{z})

- lo g_{10} (6.4 \cdot 1 0^{- 10})

- \frac{1}{2} + \frac{1}{2} ln (\frac{4 + 7}{3})

- \frac{ln ( \frac{45}{203} )}{ln ( \frac{293}{313} ) - ln ( \frac{45}{203} )}

- 2 ln (a) + \frac{1}{3} ln (b) - 3 ln (c)

What is 3log_{6}(x)+2log_{6}(y)-1/2 log_{6}(z) ?
The solution to 3log_{6}(x)+2log_{6}(y)-1/2 log_{6}(z) is log_{6}((x^3y^2sqrt(z))/z)