What is 3log_{c}(x)-1/2 log_{c}(y)+4log_{c}(w) ?

The solution to 3log_{c}(x)-1/2 log_{c}(y)+4log_{c}(w) is log_{c}((x^3w^4sqrt(y))/y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3log_{c}(x)-1/2 log_{c}(y)+4log_{c}(w)

simplify

3 lo g_{c} (x) - \frac{1}{2} lo g_{c} (y) + 4 lo g_{c} (w)

lo g_{c} (\frac{x ^{3} w ^{4} y}{y})

Solution steps

3 lo g_{c} (x) - \frac{1}{2} lo g_{c} (y) + 4 lo g_{c} (w)

Apply log rule:

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

3 lo g_{c} (x) = lo g_{c} (x^{3})

= lo g_{c} (x^{3}) - \frac{1}{2} lo g_{c} (y) + 4 lo g_{c} (w)

Apply log rule:

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

\frac{1}{2} lo g_{c} (y) = lo g_{c} (y^{\frac{1}{2}})

= lo g_{c} (x^{3}) - lo g_{c} (y^{\frac{1}{2}}) + 4 lo g_{c} (w)

Apply log rule:

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

lo g_{c} (x^{3}) - lo g_{c} (y^{\frac{1}{2}}) = lo g_{c} (\frac{x ^{3}}{y ^{\frac{1}{2}}})

= lo g_{c} (\frac{x ^{3}}{y ^{\frac{1}{2}}}) + 4 lo g_{c} (w)

Simplify

\frac{x ^{3}}{y ^{\frac{1}{2}}} : \frac{x ^{3} y}{y}

= lo g_{c} (\frac{x ^{3} y}{y}) + 4 lo g_{c} (w)

Apply log rule:

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

4 lo g_{c} (w) = lo g_{c} (w^{4})

= lo g_{c} (\frac{x ^{3} y}{y}) + lo g_{c} (w^{4})

Apply log rule:

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

lo g_{c} (\frac{x ^{3} y}{y}) + lo g_{c} (w^{4}) = lo g_{c} (\frac{x ^{3} y}{y} w^{4})

= lo g_{c} (\frac{x ^{3} y}{y} w^{4})

Simplify

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

= lo g_{c} (\frac{x ^{3} w ^{4} y}{y})

lo g_{10} (2) + lo g_{10} (125)

ln ((8 x)^{\frac{1}{2}}) + ln (4) x^{2} - ln ((16 x)^{\frac{1}{2}})

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

ln (\frac{2 x ^{3}}{( x + 4 ) ^{2}})

lo g_{a} (u^{7} v^{3})

What is 3log_{c}(x)-1/2 log_{c}(y)+4log_{c}(w) ?
The solution to 3log_{c}(x)-1/2 log_{c}(y)+4log_{c}(w) is log_{c}((x^3w^4sqrt(y))/y)