What is 4+2log_{5}(x)-1/3 log_{5}(y) ?

The solution to 4+2log_{5}(x)-1/3 log_{5}(y) is 4+log_{5}((x^2y^{2/3})/y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4+2log_{5}(x)-1/3 log_{5}(y)

simplify

4 + 2 lo g_{5} (x) - \frac{1}{3} lo g_{5} (y)

4 + lo g_{5} (\frac{x ^{2} y ^{\frac{2}{3}}}{y})

Solution steps

4 + 2 lo g_{5} (x) - \frac{1}{3} lo g_{5} (y)

Apply log rule:

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

2 lo g_{5} (x) = lo g_{5} (x^{2})

= 4 + lo g_{5} (x^{2}) - \frac{1}{3} lo g_{5} (y)

Apply log rule:

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

\frac{1}{3} lo g_{5} (y) = lo g_{5} (y^{\frac{1}{3}})

= 4 + lo g_{5} (x^{2}) - lo g_{5} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{5} (x^{2}) - lo g_{5} (y^{\frac{1}{3}}) = lo g_{5} (\frac{x ^{2}}{y ^{\frac{1}{3}}})

= 4 + lo g_{5} (\frac{x ^{2}}{y ^{\frac{1}{3}}})

Simplify

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

= 4 + lo g_{5} (\frac{x ^{2} y ^{\frac{2}{3}}}{y})

- ln (\frac{2 l + d}{l}) + ln (\frac{l + d}{l}) + ln (\frac{l + d}{d})

- lo g_{10} (7.93 \cdot 1 0^{- 3})

\frac{2}{7} lo g_{10} (a) - \frac{1}{8} lo g_{10} (b)

ln (ln (y)) + ln (x) + c

ln (\frac{432}{5})

What is 4+2log_{5}(x)-1/3 log_{5}(y) ?
The solution to 4+2log_{5}(x)-1/3 log_{5}(y) is 4+log_{5}((x^2y^{2/3})/y)