What is 6log_{c}(y)-1/3 log_{c}(w)+4log_{c}(x) ?

The solution to 6log_{c}(y)-1/3 log_{c}(w)+4log_{c}(x) is log_{c}((y^6x^4w^{2/3})/w)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 6log_{c}(y)-1/3 log_{c}(w)+4log_{c}(x)

simplify

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

lo g_{c} (\frac{y ^{6} x ^{4} w ^{\frac{2}{3}}}{w})

Solution steps

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

Apply log rule:

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

6 lo g_{c} (y) = lo g_{c} (y^{6})

= lo g_{c} (y^{6}) - \frac{1}{3} lo g_{c} (w) + 4 lo g_{c} (x)

Apply log rule:

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

\frac{1}{3} lo g_{c} (w) = lo g_{c} (w^{\frac{1}{3}})

= lo g_{c} (y^{6}) - lo g_{c} (w^{\frac{1}{3}}) + 4 lo g_{c} (x)

Apply log rule:

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

lo g_{c} (y^{6}) - lo g_{c} (w^{\frac{1}{3}}) = lo g_{c} (\frac{y ^{6}}{w ^{\frac{1}{3}}})

= lo g_{c} (\frac{y ^{6}}{w ^{\frac{1}{3}}}) + 4 lo g_{c} (x)

Simplify

\frac{y ^{6}}{w ^{\frac{1}{3}}} : \frac{y ^{6} w ^{\frac{2}{3}}}{w}

= lo g_{c} (\frac{y ^{6} w ^{\frac{2}{3}}}{w}) + 4 lo g_{c} (x)

Apply log rule:

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

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

= lo g_{c} (\frac{y ^{6} w ^{\frac{2}{3}}}{w}) + lo g_{c} (x^{4})

Apply log rule:

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

lo g_{c} (\frac{y ^{6} w ^{\frac{2}{3}}}{w}) + lo g_{c} (x^{4}) = lo g_{c} (\frac{y ^{6} w ^{\frac{2}{3}}}{w} x^{4})

= lo g_{c} (\frac{y ^{6} w ^{\frac{2}{3}}}{w} x^{4})

Simplify

\frac{y ^{6} w ^{\frac{2}{3}}}{w} x^{4} : \frac{y ^{6} x ^{4} w ^{\frac{2}{3}}}{w}

= lo g_{c} (\frac{y ^{6} x ^{4} w ^{\frac{2}{3}}}{w})

ln (x^{2} - 9) - ln (3 + x)

ln (\frac{x ^{2}}{x ^{2} - 36})

- lo g_{10} (6.37 \cdot 1 0^{- 9})

- \frac{2 ln ( 2 )}{- 2 ln ( 2 ) - 1}

- lo g_{10} (1.83 \cdot 1 0^{- 6})

What is 6log_{c}(y)-1/3 log_{c}(w)+4log_{c}(x) ?
The solution to 6log_{c}(y)-1/3 log_{c}(w)+4log_{c}(x) is log_{c}((y^6x^4w^{2/3})/w)