en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(64e^3)-ln(4e)

Solution

simplify

ln (64 e^{3}) - ln (4 e)

Solution

4 ln (2) + 2

+1

Decimal Notation

4.77258 \dots

Solution steps

ln (64 e^{3}) - ln (4 e)

Apply log rule:

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

ln (64 e^{3}) = ln (64) + ln (e^{3}), ln (4 e) = ln (4) + ln (e)

= ln (64) + ln (e^{3}) - (ln (4) + ln (e))

Apply log rule:

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

ln (e^{3}) = 3 ln (e)

= ln (64) + 3 ln (e) - (ln (4) + ln (e))

3 ln (e) = 3

- (ln (4) + ln (e)) = - (2 ln (2) + 1)

= ln (64) + 3 - (2 ln (2) + 1)

ln (64) = 6 ln (2)

= 6 ln (2) + 3 - (2 ln (2) + 1)

- (2 ln (2) + 1) : - 2 ln (2) - 1

= 6 ln (2) + 3 - 2 ln (2) - 1

Simplify

6 ln (2) + 3 - 2 ln (2) - 1 : 4 ln (2) + 2

= 4 ln (2) + 2

Popular Examples

factor ln(1/(s^2))factor

ln (\frac{1}{s ^{2}})

simplify-log_{10}(7.9*10^9)simplify

- lo g_{10} (7.9 \cdot 1 0^{9})

simplify ln(x^{-1})-ln(x)simplify

ln (x^{- 1}) - ln (x)

simplify 3log_{2}(x)-12log_{2}(y)simplify

3 lo g_{2} (x) - 12 lo g_{2} (y)

simplify log_{e}(575/500)simplify

lo g_{e} (\frac{575}{500})

Frequently Asked Questions (FAQ)

What is ln(64e^3)-ln(4e) ?
The solution to ln(64e^3)-ln(4e) is 4ln(2)+2