en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(4*4^3)

Solution

simplify

ln (4 \cdot 4^{3})

Solution

8 ln (2)

+1

Decimal Notation

5.54517 \dots

Solution steps

ln (4 \cdot 4^{3})

Apply log rule:

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

ln (4 \cdot 4^{3}) = ln (4) + ln (4^{3})

= ln (4) + ln (4^{3})

Apply log rule:

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

ln (4^{3}) = 3 ln (4)

= ln (4) + 3 ln (4)

Add similar elements:

ln (4) + 3 ln (4) = 4 ln (4)

= 4 ln (4)

Simplify

ln (4) : 2 ln (2)

= 4 \cdot 2 ln (2)

Multiply the numbers:

4 \cdot 2 = 8

= 8 ln (2)

Popular Examples

simplify 4.18*ln((355.9)/(297.38))simplify

4.18 \cdot ln (\frac{355.9}{297.38})

simplify ln(353)-ln(343)simplify

ln (353) - ln (343)

simplify 1/3 log_{2}(x)+2/3 log_{2}(y)-3 simplify

\frac{1}{3} lo g_{2} (x) + \frac{2}{3} lo g_{2} (y) - 3

simplify-0.1*ln(0.1)-(1-0.1)*ln(1-0.1)simplify

- 0.1 \cdot ln (0.1) - (1 - 0.1) \cdot ln (1 - 0.1)

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

ln (\frac{1}{t} x^{(\frac{1}{t} - 1)})

Frequently Asked Questions (FAQ)

What is ln(4*4^3) ?
The solution to ln(4*4^3) is 8ln(2)