en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(2)+1/2 ln(25)

Solution

simplify

ln (2) + \frac{1}{2} ln (25)

Solution

ln (10)

+1

Decimal Notation

2.30258 \dots

Solution steps

ln (2) + \frac{1}{2} ln (25)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (25) = ln (2 5^{\frac{1}{2}})

= ln (2) + ln (2 5^{\frac{1}{2}})

Apply log rule:

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

ln (2) + ln (2 5^{\frac{1}{2}}) = ln (2 \cdot 2 5^{\frac{1}{2}})

= ln (2 \cdot 2 5^{\frac{1}{2}})

2 \cdot 2 5^{\frac{1}{2}} = 10

= ln (10)

Popular Examples

simplify log_{10}(zy^3)simplify

lo g_{10} (z y^{3})

simplify log_{8}(t/(64))simplify

lo g_{8} (\frac{t}{64})

simplify log_{2}(x^2-1)-2log_{2}(x-1)simplify

lo g_{2} (x^{2} - 1) - 2 lo g_{2} (x - 1)

simplify log_{a}(mn^2)simplify

lo g_{a} (m n^{2})

expand log_{10}((3xyz^2)^3)expand

lo g_{10} ((3 x y z^{2})^{3})

Frequently Asked Questions (FAQ)

What is ln(2)+1/2 ln(25) ?
The solution to ln(2)+1/2 ln(25) is ln(10)