What is ln((sqrt(x^5y^8))/(x^7)) ?

The solution to ln((sqrt(x^5y^8))/(x^7)) is ln(sqrt(x)sqrt(x^4)sqrt(y^8))-7ln(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((sqrt(x^5y^8))/(x^7))

simplify

ln (\frac{x ^{5} y ^{8}}{x ^{7}})

ln (x x^{4} y^{8}) - 7 ln (x)

Solution steps

ln (\frac{x ^{5} y ^{8}}{x ^{7}})

Apply log rule:

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

ln (\frac{x ^{5} y ^{8}}{x ^{7}}) = ln (x^{5} y^{8}) - ln (x^{7})

= ln (x^{5} y^{8}) - ln (x^{7})

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= ln (x^{5} y^{8}) - 7 ln (x)

x^{5} y^{8} = x x^{4} y^{8}

= ln (x x^{4} y^{8}) - 7 ln (x)

- lo g_{10} (3 \times 1 0^{- 8})

lo g_{3} (25) + lo g_{3} (4)

lo g_{2} (3) + 2 lo g_{2} (5)

ln (- 3 y)

- lo g_{10} (3 \cdot 1 0^{- 6})

What is ln((sqrt(x^5y^8))/(x^7)) ?
The solution to ln((sqrt(x^5y^8))/(x^7)) is ln(sqrt(x)sqrt(x^4)sqrt(y^8))-7ln(x)