What is log_{b}(4x)+7(log_{b}(x)-log_{b}(y)) ?

The solution to log_{b}(4x)+7(log_{b}(x)-log_{b}(y)) is log_{b}((4x^8)/(y^7))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{b}(4x)+7(log_{b}(x)-log_{b}(y))

simplify

lo g_{b} (4 x) + 7 (lo g_{b} (x) - lo g_{b} (y))

lo g_{b} (\frac{4 x ^{8}}{y ^{7}})

Solution steps

lo g_{b} (4 x) + 7 (lo g_{b} (x) - lo g_{b} (y))

Apply log rule:

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

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

= lo g_{b} (4 x) + 7 lo g_{b} (\frac{x}{y})

Apply log rule:

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

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

= lo g_{b} (4 x) + lo g_{b} ((\frac{x}{y})^{7})

Apply log rule:

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

lo g_{b} (4 x) + lo g_{b} ((\frac{x}{y})^{7}) = lo g_{b} (4 (\frac{x}{y})^{7} x)

= lo g_{b} (4 (\frac{x}{y})^{7} x)

Simplify

4 x (\frac{x}{y})^{7} : \frac{4 x ^{8}}{y ^{7}}

= lo g_{b} (\frac{4 x ^{8}}{y ^{7}})

\frac{1}{3} \cdot lo g_{4} (8) + lo g_{4} (15)

2 lo g_{b} (x) + 7 lo g_{b} (z)

lo g_{4} (\frac{ab}{c d})

ln (x - 2) - ln (2 x - 3)

lo g_{10} (5 x) - 7 (10 x - 2)

What is log_{b}(4x)+7(log_{b}(x)-log_{b}(y)) ?
The solution to log_{b}(4x)+7(log_{b}(x)-log_{b}(y)) is log_{b}((4x^8)/(y^7))