What is log_{10}((m^n)*(p^q)) ?

The solution to log_{10}((m^n)*(p^q)) is nlog_{10}(m)+qlog_{10}(p)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}((m^n)*(p^q))

simplify

lo g_{10} ((m^{n}) \cdot (p^{q}))

n lo g_{10} (m) + q lo g_{10} (p)

Solution steps

lo g_{10} ((m^{n}) (p^{q}))

Simplify

(m^{n}) (p^{q}) : m^{n} p^{q}

= lo g_{10} (m^{n} p^{q})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (m^{n} p^{q}) = lo g_{10} (m^{n}) + lo g_{10} (p^{q})

= lo g_{10} (m^{n}) + lo g_{10} (p^{q})

lo g_{10} (m^{n}) = n lo g_{10} (m)

lo g_{10} (p^{q}) = q lo g_{10} (p)

= n lo g_{10} (m) + q lo g_{10} (p)

7 lo g_{2} (u) + 4 lo g_{2} (v)

ln (\frac{e ^{9}}{7})

lo g_{4} (8) + lo g_{4} (x)

lo g_{t} (6 t)

ln (\frac{2 \cdot e ^{- 1} + e ^{- 1} 1 + \frac{e ^{- 1} 1 ^{2}}{2}}{5})

What is log_{10}((m^n)*(p^q)) ?
The solution to log_{10}((m^n)*(p^q)) is nlog_{10}(m)+qlog_{10}(p)