What is log_{10}(x)-1/4 log_{10}(y)+4log_{10}(z) ?

The solution to log_{10}(x)-1/4 log_{10}(y)+4log_{10}(z) is log_{10}((xz^4y^{3/4})/y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(x)-1/4 log_{10}(y)+4log_{10}(z)

simplify

lo g_{10} (x) - \frac{1}{4} lo g_{10} (y) + 4 lo g_{10} (z)

lo g_{10} (\frac{x z ^{4} y ^{\frac{3}{4}}}{y})

Solution steps

lo g_{10} (x) - \frac{1}{4} lo g_{10} (y) + 4 lo g_{10} (z)

Apply log rule:

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

\frac{1}{4} lo g_{10} (y) = lo g_{10} (y^{\frac{1}{4}})

= lo g_{10} (x) - lo g_{10} (y^{\frac{1}{4}}) + 4 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^{\frac{1}{4}}) = lo g_{10} (\frac{x}{y ^{\frac{1}{4}}})

= lo g_{10} (\frac{x}{y ^{\frac{1}{4}}}) + 4 lo g_{10} (z)

Simplify

\frac{x}{y ^{\frac{1}{4}}} : \frac{x y ^{\frac{3}{4}}}{y}

= lo g_{10} (\frac{x y ^{\frac{3}{4}}}{y}) + 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} (\frac{x y ^{\frac{3}{4}}}{y}) + lo g_{10} (z^{4})

Apply log rule:

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

lo g_{10} (\frac{x y ^{\frac{3}{4}}}{y}) + lo g_{10} (z^{4}) = lo g_{10} (\frac{x y ^{\frac{3}{4}}}{y} z^{4})

= lo g_{10} (\frac{x y ^{\frac{3}{4}}}{y} z^{4})

Simplify

\frac{x y ^{\frac{3}{4}}}{y} z^{4} : \frac{x z ^{4} y ^{\frac{3}{4}}}{y}

= lo g_{10} (\frac{x z ^{4} y ^{\frac{3}{4}}}{y})

lo g_{10} (4 x^{5})

lo g_{2} (\frac{32}{x y ^{2}})

\frac{3}{4} ln (x) + ln (x^{2} + 1) - 7 ln (4 x + 5)

α ln (\frac{α q}{α + 1}) + ln (\frac{q}{( α + 1 ) ^{2}})

lo g_{4} (4 x) + 2 lo g_{4} (4)

What is log_{10}(x)-1/4 log_{10}(y)+4log_{10}(z) ?
The solution to log_{10}(x)-1/4 log_{10}(y)+4log_{10}(z) is log_{10}((xz^4y^{3/4})/y)