What is factor log_{3}(sqrt(x))-log_{3}(x^7) ?

The solution to factor log_{3}(sqrt(x))-log_{3}(x^7) is -log_{3}(x^{13/2})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor log_{3}(sqrt(x))-log_{3}(x^7)

factor

lo g_{3} (x) - lo g_{3} (x^{7})

- lo g_{3} (x^{\frac{13}{2}})

Solution steps

lo g_{3} (x) - lo g_{3} (x^{7})

Apply log rule:

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

lo g_{3} (x) - lo g_{3} (x^{7}) = lo g_{3} (\frac{x}{x ^{7}})

= lo g_{3} (\frac{x}{x ^{7}})

Factor

\frac{x}{x ^{7}} : \frac{1}{x ^{\frac{13}{2}}}

= lo g_{3} (\frac{1}{x ^{\frac{13}{2}}})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - lo g_{3} (x^{\frac{13}{2}})

- \frac{1}{20} ln (\frac{1}{2})

lo g_{3} (11) - lo g_{3} (4)

lo g_{3} (x) + lo g_{3} (2 x)

lo g_{7} (49 n)

lo g_{10} (30) + lo g_{10} (6)

What is factor log_{3}(sqrt(x))-log_{3}(x^7) ?
The solution to factor log_{3}(sqrt(x))-log_{3}(x^7) is -log_{3}(x^{13/2})