en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2-2ln(2)+2ln(x)

Solution

simplify

2 - 2 ln (2) + 2 ln (x)

Solution

2 + ln (\frac{x ^{2}}{4})

Solution steps

2 - 2 ln (2) + 2 ln (x)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{2}) - ln (2^{2}) = ln (\frac{x ^{2}}{2 ^{2}})

= 2 + ln (\frac{x ^{2}}{2 ^{2}})

2^{2} = 4

= 2 + ln (\frac{x ^{2}}{4})

Popular Examples

simplify log_{10}(810)+log_{10}(0.03)simplify

lo g_{10} (810) + lo g_{10} (0.03)

simplify-1/3 (ln(26)-ln(5))simplify

- \frac{1}{3} (ln (26) - ln (5))

expand ln(1/(sqrt(t)))expand

ln (\frac{1}{t})

simplify ln|4|-ln(x)simplify

ln ∣ 4 ∣ - ln (x)

simplify log_{e}(1/12)simplify

lo g_{e} (\frac{1}{12})

Frequently Asked Questions (FAQ)

What is 2-2ln(2)+2ln(x) ?
The solution to 2-2ln(2)+2ln(x) is 2+ln((x^2)/4)