What is simplify-ln((e^a)/b) ?

The solution to simplify-ln((e^a)/b) is -a+ln(b)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-ln((e^a)/b)

simplify

- ln (\frac{e ^{a}}{b})

- a + ln (b)

Solution steps

- ln (\frac{e ^{a}}{b})

Apply log rule:

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

ln (\frac{e ^{a}}{b}) = ln (e^{a}) - ln (b)

= - (ln (e^{a}) - ln (b))

Apply log rule:

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

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

= - (a ln (e) - ln (b))

a ln (e) = a

= - (a - ln (b))

Distribute parentheses

= - (a) - (- ln (b))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - a + ln (b)

- lo g_{10} (9.08 \cdot 1 0^{- 6})

3 t + ln (5 - y) - ln (y) - 2 ln (2)

ln (e^{x^{3}}) - ln (x^{4} - 7 x + 1)

4 [ln (x) - ln (x + 7) - ln (x - 7)]

ln (\frac{x c}{m})