What is 2log_{6}(x)+1/2 log_{6}(y)-2-7log_{6}(z) ?

The solution to 2log_{6}(x)+1/2 log_{6}(y)-2-7log_{6}(z) is log_{6}((x^2y^{1/2})/(z^7))-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2log_{6}(x)+1/2 log_{6}(y)-2-7log_{6}(z)

simplify

2 lo g_{6} (x) + \frac{1}{2} lo g_{6} (y) - 2 - 7 lo g_{6} (z)

lo g_{6} (\frac{x ^{2} y ^{\frac{1}{2}}}{z ^{7}}) - 2

Solution steps

2 lo g_{6} (x) + \frac{1}{2} lo g_{6} (y) - 2 - 7 lo g_{6} (z)

Apply log rule:

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

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

= lo g_{6} (x^{2}) + \frac{1}{2} lo g_{6} (y) - 2 - 7 lo g_{6} (z)

Apply log rule:

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

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

= lo g_{6} (x^{2}) + lo g_{6} (y^{\frac{1}{2}}) - 2 - 7 lo g_{6} (z)

Apply log rule:

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

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

= lo g_{6} (x^{2} y^{\frac{1}{2}}) - 2 - 7 lo g_{6} (z)

Apply log rule:

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

7 lo g_{6} (z) = lo g_{6} (z^{7})

= lo g_{6} (x^{2} y^{\frac{1}{2}}) - 2 - lo g_{6} (z^{7})

Apply log rule:

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

lo g_{6} (x^{2} y^{\frac{1}{2}}) - lo g_{6} (z^{7}) = lo g_{6} (\frac{x ^{2} y ^{\frac{1}{2}}}{z ^{7}})

= lo g_{6} (\frac{x ^{2} y ^{\frac{1}{2}}}{z ^{7}}) - 2

lo g_{2} (75) - 2 lo g_{2} (5)

ln (x) + ln (x + 8)

lo g_{a} (2 x)

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

What is 2log_{6}(x)+1/2 log_{6}(y)-2-7log_{6}(z) ?
The solution to 2log_{6}(x)+1/2 log_{6}(y)-2-7log_{6}(z) is log_{6}((x^2y^{1/2})/(z^7))-2