What is 6log_{10}(x)-1/3 log_{10}(y) ?

The solution to 6log_{10}(x)-1/3 log_{10}(y) is log_{10}((x^6y^{2/3})/y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 6log_{10}(x)-1/3 log_{10}(y)

simplify

6 lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

lo g_{10} (\frac{x ^{6} y ^{\frac{2}{3}}}{y})

Solution steps

6 lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

Apply log rule:

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

6 lo g_{10} (x) = lo g_{10} (x^{6})

= lo g_{10} (x^{6}) - \frac{1}{3} lo g_{10} (y)

Apply log rule:

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

\frac{1}{3} lo g_{10} (y) = lo g_{10} (y^{\frac{1}{3}})

= lo g_{10} (x^{6}) - lo g_{10} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{10} (x^{6}) - lo g_{10} (y^{\frac{1}{3}}) = lo g_{10} (\frac{x ^{6}}{y ^{\frac{1}{3}}})

= lo g_{10} (\frac{x ^{6}}{y ^{\frac{1}{3}}})

Simplify

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

= lo g_{10} (\frac{x ^{6} y ^{\frac{2}{3}}}{y})

ln (ln (\frac{1}{1 - 0.03})) - ln (ln (\frac{1}{1 - 0.008}))

ln (\frac{x}{cos ( x )})

\frac{π ^{2}}{2} ln (2)

5 lo g_{10} (x) - 4 lo g_{10} (x + 5)

ln (\frac{0.3}{0.1})

What is 6log_{10}(x)-1/3 log_{10}(y) ?
The solution to 6log_{10}(x)-1/3 log_{10}(y) is log_{10}((x^6y^{2/3})/y)