What is log_{10}(x)+5log_{10}(y)-4log_{10}(z) ?

The solution to log_{10}(x)+5log_{10}(y)-4log_{10}(z) is log_{10}((xy^5)/(z^4))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(x)+5log_{10}(y)-4log_{10}(z)

simplify

lo g_{10} (x) + 5 lo g_{10} (y) - 4 lo g_{10} (z)

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

Solution steps

lo g_{10} (x) + 5 lo g_{10} (y) - 4 lo g_{10} (z)

Apply log rule:

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

5 lo g_{10} (y) = lo g_{10} (y^{5})

= lo g_{10} (x) + lo g_{10} (y^{5}) - 4 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x) + lo g_{10} (y^{5}) = lo g_{10} (x y^{5})

= lo g_{10} (x y^{5}) - 4 lo g_{10} (z)

Apply log rule:

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

4 lo g_{10} (z) = lo g_{10} (z^{4})

= lo g_{10} (x y^{5}) - lo g_{10} (z^{4})

Apply log rule:

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

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

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

2 ln (x) - \frac{1}{2} ln (y)

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

lo g_{3} (7) + \frac{1}{2} lo g_{3} (t) - lo g_{3} (r)

\frac{1}{2} \cdot ln (2)

lo g_{10} (\frac{100 x ^{2}}{27})

What is log_{10}(x)+5log_{10}(y)-4log_{10}(z) ?
The solution to log_{10}(x)+5log_{10}(y)-4log_{10}(z) is log_{10}((xy^5)/(z^4))