What is (log_{b}(x)-log_{b}(y))+7log_{b}(v) ?

The solution to (log_{b}(x)-log_{b}(y))+7log_{b}(v) is log_{b}((xv^7)/y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (log_{b}(x)-log_{b}(y))+7log_{b}(v)

simplify

(lo g_{b} (x) - lo g_{b} (y)) + 7 lo g_{b} (v)

lo g_{b} (\frac{x v ^{7}}{y})

Solution steps

(lo g_{b} (x) - lo g_{b} (y)) + 7 lo g_{b} (v)

Apply rule:

(a) = a

(lo g_{b} (x) - lo g_{b} (y)) = lo g_{b} (x) - lo g_{b} (y)

= lo g_{b} (x) - lo g_{b} (y) + 7 lo g_{b} (v)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

7 lo g_{b} (v) = lo g_{b} (v^{7})

= lo g_{b} (x) - lo g_{b} (y) + lo g_{b} (v^{7})

Apply log rule:

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

lo g_{b} (x) - lo g_{b} (y) = lo g_{b} (\frac{x}{y})

= lo g_{b} (\frac{x}{y}) + lo g_{b} (v^{7})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{b} (\frac{x}{y}) + lo g_{b} (v^{7}) = lo g_{b} (\frac{x}{y} v^{7})

= lo g_{b} (\frac{x}{y} v^{7})

Simplify

\frac{x}{y} v^{7} : \frac{x v ^{7}}{y}

= lo g_{b} (\frac{x v ^{7}}{y})

4 ln (x) + 3 ln (y) - 2 ln (z)

lo g_{2} (16 x^{3})

- ln (a) + ln (b)

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

What is (log_{b}(x)-log_{b}(y))+7log_{b}(v) ?
The solution to (log_{b}(x)-log_{b}(y))+7log_{b}(v) is log_{b}((xv^7)/y)