en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(4)+ln(x)-3ln(2)

Solution

simplify

ln (4) + ln (x) - 3 ln (2)

Solution

ln (\frac{x}{2})

Solution steps

ln (4) + ln (x) - 3 ln (2)

Apply log rule:

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

ln (4) + ln (x) = ln (4 x)

= ln (4 x) - 3 ln (2)

Apply log rule:

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

3 ln (2) = ln (2^{3})

= ln (4 x) - ln (2^{3})

Apply log rule:

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

ln (4 x) - ln (2^{3}) = ln (\frac{4 x}{2 ^{3}})

= ln (\frac{4 x}{2 ^{3}})

Simplify

\frac{4 x}{2 ^{3}} : \frac{x}{2}

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

Popular Examples

simplify log_{10}(x)+log_{10}(x+9)simplify

lo g_{10} (x) + lo g_{10} (x + 9)

join 4/5 ln(2)join

\frac{4}{5} ln (2)

simplify log_{6}(sqrt(x))-log_{6}(x^3)simplify

lo g_{6} (x) - lo g_{6} (x^{3})

simplify log_{b}(9)+log_{b}(8)simplify

lo g_{b} (9) + lo g_{b} (8)

simplify ln(5)+3ln(x)+4ln(x^2+4)simplify

ln (5) + 3 ln (x) + 4 ln (x^{2} + 4)

Frequently Asked Questions (FAQ)

What is ln(4)+ln(x)-3ln(2) ?
The solution to ln(4)+ln(x)-3ln(2) is ln(x/2)