en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(ae^x)

Solution

simplify

ln (a e^{x})

Solution

ln (a) + x

Solution steps

ln (a e^{x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (a) + x ln (e)

x ln (e) = x

= ln (a) + x

Popular Examples

simplify log_{2}(x)-log_{2}(y)simplify

lo g_{2} (x) - lo g_{2} (y)

simplify log_{10}(x/(x-1))simplify

lo g_{10} (\frac{x}{x - 1})

simplify 3log_{10}(5)+2log_{10}(3)-4log_{10}(2)simplify

3 lo g_{10} (5) + 2 lo g_{10} (3) - 4 lo g_{10} (2)

simplify-log_{10}(4*10^{-4})simplify

- lo g_{10} (4 \cdot 1 0^{- 4})

simplify log_{5}((3y)/(\sqrt[4]{2x)})simplify

Frequently Asked Questions (FAQ)

What is ln(ae^x) ?
The solution to ln(ae^x) is ln(a)+x