What is 2log_{10}(x)-5log_{10}(y)+3log_{10}(z) ?

The solution to 2log_{10}(x)-5log_{10}(y)+3log_{10}(z) is log_{10}((x^2z^3)/(y^5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2log_{10}(x)-5log_{10}(y)+3log_{10}(z)

simplify

2 lo g_{10} (x) - 5 lo g_{10} (y) + 3 lo g_{10} (z)

lo g_{10} (\frac{x ^{2} z ^{3}}{y ^{5}})

Solution steps

2 lo g_{10} (x) - 5 lo g_{10} (y) + 3 lo g_{10} (z)

Apply log rule:

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

2 lo g_{10} (x) = lo g_{10} (x^{2})

= lo g_{10} (x^{2}) - 5 lo g_{10} (y) + 3 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^{2}) - lo g_{10} (y^{5}) + 3 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{2}) - lo g_{10} (y^{5}) = lo g_{10} (\frac{x ^{2}}{y ^{5}})

= lo g_{10} (\frac{x ^{2}}{y ^{5}}) + 3 lo g_{10} (z)

Apply log rule:

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

3 lo g_{10} (z) = lo g_{10} (z^{3})

= lo g_{10} (\frac{x ^{2}}{y ^{5}}) + lo g_{10} (z^{3})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{y ^{5}}) + lo g_{10} (z^{3}) = lo g_{10} (\frac{x ^{2}}{y ^{5}} z^{3})

= lo g_{10} (\frac{x ^{2}}{y ^{5}} z^{3})

Multiply fractions:

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

= lo g_{10} (\frac{x ^{2} z ^{3}}{y ^{5}})

lo g_{5} (40) + lo g_{5} (8)

lo g_{10} (\frac{a \cdot b}{c})

lo g_{2} (7) + lo g_{2} (x) - lo g_{2} (7)

lo g_{10} (\frac{y}{2})

ln (6 x)

What is 2log_{10}(x)-5log_{10}(y)+3log_{10}(z) ?
The solution to 2log_{10}(x)-5log_{10}(y)+3log_{10}(z) is log_{10}((x^2z^3)/(y^5))