en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(2^x)+ln(e^x)

Solution

simplify

ln (2^{x}) + ln (e^{x})

Solution

ln (2 e) x

Solution steps

ln (2^{x}) + ln (e^{x})

Apply log rule:

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

ln (2^{x}) + ln (e^{x}) = ln (2^{x} e^{x})

= ln (2^{x} e^{x})

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

2^{x} e^{x} = (2 e)^{x}

= ln ((2 e)^{x})

Apply log rule

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

assuming

x \geq 0

= ln (2 e) x

Popular Examples

simplify 10ln(1/199)simplify

10 ln (\frac{1}{199})

simplify 0.5log_{3}(6)-0.25log_{3}(4)simplify

0.5 lo g_{3} (6) - 0.25 lo g_{3} (4)

simplify ln(2.46)-ln(17.39)simplify

ln (2.46) - ln (17.39)

simplify-log_{10}(6.18*10^{-6})simplify

- lo g_{10} (6.18 \cdot 1 0^{- 6})

simplify 1/3 ln(8/5)simplify

\frac{1}{3} ln (\frac{8}{5})

Frequently Asked Questions (FAQ)

What is ln(2^x)+ln(e^x) ?
The solution to ln(2^x)+ln(e^x) is ln(2e)x