en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(8x)-ln(2x)

Solution

simplify

ln (8 x) - ln (2 x)

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

ln (8 x) - ln (2 x)

Apply log rule:

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

ln (8 x) - ln (2 x) = ln (\frac{8 x}{2 x})

= ln (\frac{8 x}{2 x})

\frac{8 x}{2 x} = 4

= ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

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

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

= 2 ln (2)

Popular Examples

simplify ln(1/((r-1)!)θ^{-w}x^{w-1}e^{-xθ^{-1}})simplify

ln (\frac{1}{( r - 1 ) !} θ^{- w} x^{w - 1} e^{- x θ^{- 1}})

simplify-1/(sqrt(2))ln(1/(sqrt(2)))+1/(sqrt(2))simplify

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

simplify log_{6}(2x)-log_{6}(x-3)3 simplify

lo g_{6} (2 x) - lo g_{6} (x - 3) 3

join (24)/pi ln(2+sqrt(3))join

\frac{24}{π} ln (2 + 3)

simplify-(-ln(x+1)+ln(x-1))simplify

- (- ln (x + 1) + ln (x - 1))

Frequently Asked Questions (FAQ)

What is ln(8x)-ln(2x) ?
The solution to ln(8x)-ln(2x) is 2ln(2)