What is log_{10}(x)-5log_{10}(y)+7log_{10}(z) ?

The solution to log_{10}(x)-5log_{10}(y)+7log_{10}(z) is log_{10}((xz^7)/(y^5))

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)+7log_{10}(z)

simplify

lo g_{10} (x) - 5 lo g_{10} (y) + 7 lo g_{10} (z)

lo g_{10} (\frac{x z ^{7}}{y ^{5}})

Solution steps

lo g_{10} (x) - 5 lo g_{10} (y) + 7 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}) + 7 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) - lo g_{10} (y^{5}) = lo g_{10} (\frac{x}{y ^{5}})

= lo g_{10} (\frac{x}{y ^{5}}) + 7 lo g_{10} (z)

Apply log rule:

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

7 lo g_{10} (z) = lo g_{10} (z^{7})

= lo g_{10} (\frac{x}{y ^{5}}) + lo g_{10} (z^{7})

Apply log rule:

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

lo g_{10} (\frac{x}{y ^{5}}) + lo g_{10} (z^{7}) = lo g_{10} (\frac{x}{y ^{5}} z^{7})

= lo g_{10} (\frac{x}{y ^{5}} z^{7})

Multiply fractions:

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

= lo g_{10} (\frac{x z ^{7}}{y ^{5}})

- [- \frac{3}{10} ln (3) + \frac{8}{35} ln (8) + \frac{15}{14} ln (1)]

lo g_{10} (x^{2} - 7 x - 8) - lo g_{10} (x^{2} - 1)

ln (\frac{( c ^{1 - n} m ^{n} ) ^{1 - l}}{1 - l})

20 lo g_{10} (2) + 40 lo g_{10} (0.04)

What is log_{10}(x)-5log_{10}(y)+7log_{10}(z) ?
The solution to log_{10}(x)-5log_{10}(y)+7log_{10}(z) is log_{10}((xz^7)/(y^5))