en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((4e^6)/(7y))

Solution

simplify

ln (\frac{4 e ^{6}}{7 y})

Solution

2 ln (2) + 6 - ln (7) - ln (y)

Solution steps

ln (\frac{4 e ^{6}}{7 y})

Apply log rule:

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

ln (\frac{4 e ^{6}}{7 y}) = ln (4 e^{6}) - ln (7 y)

= ln (4 e^{6}) - ln (7 y)

Apply log rule:

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

ln (4 e^{6}) = ln (4) + ln (e^{6}), ln (7 y) = ln (7) + ln (y)

= ln (4) + ln (e^{6}) - (ln (y) + ln (7))

Apply log rule:

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

ln (e^{6}) = 6 ln (e)

= ln (4) + 6 ln (e) - (ln (7) + ln (y))

6 ln (e) = 6

= ln (4) + 6 - (ln (y) + ln (7))

ln (4) = 2 ln (2)

= 2 ln (2) + 6 - (ln (y) + ln (7))

- (ln (7) + ln (y)) : - ln (7) - ln (y)

= 2 ln (2) + 6 - ln (7) - ln (y)

Popular Examples

simplify log_{7}(sqrt(x))-log_{7}(x^2)simplify

lo g_{7} (x) - lo g_{7} (x^{2})

simplify ln(x/b)simplify

ln (\frac{x}{b})

expand log_{10}((zx^2)/(\sqrt[3]{y^2)})expand

simplify 1/2 log_{10}(3)-1/2 log_{10}(12)simplify

\frac{1}{2} lo g_{10} (3) - \frac{1}{2} lo g_{10} (12)

simplify ln(x/e)simplify

ln (\frac{x}{e})

Frequently Asked Questions (FAQ)

What is ln((4e^6)/(7y)) ?
The solution to ln((4e^6)/(7y)) is 2ln(2)+6-ln(7)-ln(y)