en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((e^5)/8)

Solution

simplify

ln (\frac{e ^{5}}{8})

Solution

5 - 3 ln (2)

+1

Decimal Notation

2.92055 \dots

Solution steps

ln (\frac{e ^{5}}{8})

Apply log rule:

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

ln (\frac{e ^{5}}{8}) = ln (e^{5}) - ln (8)

= ln (e^{5}) - ln (8)

Apply log rule:

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

ln (e^{5}) = 5 ln (e)

= 5 ln (e) - ln (8)

5 ln (e) = 5

= 5 - ln (8)

ln (8) = 3 ln (2)

= 5 - 3 ln (2)

Popular Examples

simplify 2*log_{10}(10x)simplify

2 \cdot lo g_{10} (10 x)

expand ln((e^2)/5)expand

ln (\frac{e ^{2}}{5})

simplify log_{10}(x)+log_{10}(34)simplify

lo g_{10} (x) + lo g_{10} (34)

simplify log_{10}(Ax^n)simplify

lo g_{10} (A x^{n})

simplify log_{5}(50)-log_{5}(0.4)simplify

lo g_{5} (50) - lo g_{5} (0.4)

Frequently Asked Questions (FAQ)

What is ln((e^5)/8) ?
The solution to ln((e^5)/8) is 5-3ln(2)