What is log_{a}(2x)+2(log_{a}(x)-log_{a}(y)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{a}(2x)+2(log_{a}(x)-log_{a}(y))

simplify

lo g_{a} (2 x) + 2 (lo g_{a} (x) - lo g_{a} (y))

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

Solution steps

lo g_{a} (2 x) + 2 (lo g_{a} (x) - lo g_{a} (y))

Apply log rule:

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

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

= lo g_{a} (2 x) + 2 lo g_{a} (\frac{x}{y})

Apply log rule:

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

2 lo g_{a} (\frac{x}{y}) = lo g_{a} ((\frac{x}{y})^{2})

= lo g_{a} (2 x) + lo g_{a} ((\frac{x}{y})^{2})

Apply log rule:

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

lo g_{a} (2 x) + lo g_{a} ((\frac{x}{y})^{2}) = lo g_{a} (2 (\frac{x}{y})^{2} x)

= lo g_{a} (2 (\frac{x}{y})^{2} x)

Simplify

2 x (\frac{x}{y})^{2} : \frac{2 x ^{3}}{y ^{2}}

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

1 + 2 lo g_{10} (x) - lo g_{10} (y)

- lo g_{10} (3.3 \cdot 1 0^{- 11})

ln (5 x) + ln (2 y^{3}) - ln (x^{2} y)

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

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