en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((ex^8)/y)

Solution

simplify

ln (\frac{e x ^{8}}{y})

Solution

1 + 8 ln (x) - ln (y)

Solution steps

ln (\frac{e x ^{8}}{y})

Apply log rule:

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

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

= ln (e x^{8}) - ln (y)

Apply log rule:

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

ln (e x^{8}) = ln (e) + ln (x^{8})

= ln (e) + ln (x^{8}) - ln (y)

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= ln (e) + 8 ln (x) - ln (y)

Apply log rule:

lo g_{a} (a) = 1

= 1 + 8 ln (x) - ln (y)

Popular Examples

expand log_{6}(36x^7)expand

lo g_{6} (36 x^{7})

simplify log_{3}(a)+log_{3}(a+6)simplify

lo g_{3} (a) + lo g_{3} (a + 6)

simplify log_{3}(a)+log_{3}(a+9)simplify

lo g_{3} (a) + lo g_{3} (a + 9)

simplify ln(x^6sqrt(6-x))simplify

ln (x^{6} 6 - x)

simplify log_{2}(1/4 mn^3)simplify

lo g_{2} (\frac{1}{4} m n^{3})

Frequently Asked Questions (FAQ)

What is ln((ex^8)/y) ?
The solution to ln((ex^8)/y) is 1+8ln(x)-ln(y)