What is 3(log_{5}(x)+3log_{5}(y)-5log_{5}(z)) ?

The solution to 3(log_{5}(x)+3log_{5}(y)-5log_{5}(z)) is 3log_{5}((xy^3)/(z^5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3(log_{5}(x)+3log_{5}(y)-5log_{5}(z))

simplify

3 (lo g_{5} (x) + 3 lo g_{5} (y) - 5 lo g_{5} (z))

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

Solution steps

3 (lo g_{5} (x) + 3 lo g_{5} (y) - 5 lo g_{5} (z))

Apply log rule:

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

3 lo g_{5} (y) = lo g_{5} (y^{3})

= 3 (lo g_{5} (x) + lo g_{5} (y^{3}) - 5 lo g_{5} (z))

Apply log rule:

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

lo g_{5} (x) + lo g_{5} (y^{3}) = lo g_{5} (x y^{3})

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

Apply log rule:

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

5 lo g_{5} (z) = lo g_{5} (z^{5})

= 3 (- lo g_{5} (z^{5}) + lo g_{5} (x y^{3}))

Apply log rule:

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

lo g_{5} (x y^{3}) - lo g_{5} (z^{5}) = lo g_{5} (\frac{x y ^{3}}{z ^{5}})

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

lo g_{5} (x^{2})

lo g_{e} (\frac{7}{2})

\frac{9}{4} ln (\frac{9}{4})

lo g_{a} (u^{8} v^{5})

lo g_{4} (7) - lo g_{4} (3)

What is 3(log_{5}(x)+3log_{5}(y)-5log_{5}(z)) ?
The solution to 3(log_{5}(x)+3log_{5}(y)-5log_{5}(z)) is 3log_{5}((xy^3)/(z^5))