What is 21log_{10}(x)-5log_{10}(q)+log_{10}(z^2) ?

The solution to 21log_{10}(x)-5log_{10}(q)+log_{10}(z^2) is log_{10}((x^{21}z^2)/(q^5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 21log_{10}(x)-5log_{10}(q)+log_{10}(z^2)

simplify

21 lo g_{10} (x) - 5 lo g_{10} (q) + lo g_{10} (z^{2})

lo g_{10} (\frac{x ^{21} z ^{2}}{q ^{5}})

Solution steps

21 lo g_{10} (x) - 5 lo g_{10} (q) + lo g_{10} (z^{2})

Apply log rule:

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

21 lo g_{10} (x) = lo g_{10} (x^{21})

= lo g_{10} (x^{21}) - 5 lo g_{10} (q) + lo g_{10} (z^{2})

Apply log rule:

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

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

= lo g_{10} (x^{21}) - lo g_{10} (q^{5}) + lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (x^{21}) - lo g_{10} (q^{5}) = lo g_{10} (\frac{x ^{21}}{q ^{5}})

= lo g_{10} (\frac{x ^{21}}{q ^{5}}) + lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (\frac{x ^{21}}{q ^{5}}) + lo g_{10} (z^{2}) = lo g_{10} (\frac{x ^{21}}{q ^{5}} z^{2})

= lo g_{10} (\frac{x ^{21}}{q ^{5}} z^{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{10} (\frac{x ^{21} z ^{2}}{q ^{5}})

lo g_{10} (4) + lo g_{10} (8)

lo g_{10} (4) + lo g_{10} (5) + lo g_{10} (3)

lo g_{2} (2 x) - lo g_{2} (x + 1)

ln (\frac{e}{4})

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

What is 21log_{10}(x)-5log_{10}(q)+log_{10}(z^2) ?
The solution to 21log_{10}(x)-5log_{10}(q)+log_{10}(z^2) is log_{10}((x^{21}z^2)/(q^5))