What is expand log_{e}((6x^2)/(y^4)) ?

The solution to expand log_{e}((6x^2)/(y^4)) is ln(6)+2ln(x)-4ln(y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{e}((6x^2)/(y^4))

expand

lo g_{e} (\frac{6 x ^{2}}{y ^{4}})

ln (6) + 2 ln (x) - 4 ln (y)

Solution steps

lo g_{e} (\frac{6 x ^{2}}{y ^{4}})

Apply log rule:

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

lo g_{e} (\frac{6 x ^{2}}{y ^{4}}) = lo g_{e} (6 x^{2}) - lo g_{e} (y^{4})

= lo g_{e} (6 x^{2}) - lo g_{e} (y^{4})

Apply log rule:

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

lo g_{e} (y^{4}) = 4 lo g_{e} (y)

= lo g_{e} (6 x^{2}) - 4 lo g_{e} (y)

Apply log rule:

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

lo g_{e} (6 x^{2}) = lo g_{e} (6) + lo g_{e} (x^{2})

= lo g_{e} (6) + lo g_{e} (x^{2}) - 4 lo g_{e} (y)

Apply log rule:

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

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

= lo g_{e} (6) + 2 lo g_{e} (x) - 4 lo g_{e} (y)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (6) + 2 lo g_{e} (x) - 4 lo g_{e} (y)

Simplify

lo g_{e} (x) : ln (x)

= ln (6) + 2 ln (x) - 4 lo g_{e} (y)

Simplify

lo g_{e} (y) : ln (y)

= ln (6) + 2 ln (x) - 4 ln (y)

0.0259 \cdot ln (\frac{4 \cdot 1 0 ^{15}}{1.5 \cdot 1 0 ^{10}})

ln (\frac{( \frac{0.302}{0.303} )}{9.9})

ln (e^{x} x^{2})

1004.5 \cdot ln (\frac{690}{288}) - 287 \cdot ln (8.656)

- lo g_{10} (4.7 \cdot 1 0^{- 11})

What is expand log_{e}((6x^2)/(y^4)) ?
The solution to expand log_{e}((6x^2)/(y^4)) is ln(6)+2ln(x)-4ln(y)