What is ln(sqrt(3x))-ln(sqrt(x)) ?

The solution to ln(sqrt(3x))-ln(sqrt(x)) is 1/2 ln(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(sqrt(3x))-ln(sqrt(x))

simplify

ln (3 x) - ln (x)

\frac{1}{2} ln (3)

Decimal Notation

0.54930 \dots

Solution steps

ln (3 x) - ln (x)

Apply log rule:

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

ln (3 x) - ln (x) = ln (\frac{3 x}{x})

= ln (\frac{3 x}{x})

\frac{3 x}{x} = 3

= ln (3)

Rewrite as

= ln (3^{\frac{1}{2}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} ln (3)

ln (x e^{(7 x)})

lo g_{10} (20) + lo g_{10} (\frac{1}{10})

\frac{5}{6} lo g_{2} (\frac{5}{6}) + \frac{1}{6} lo g_{2} (\frac{1}{6})

6 lo g_{2} (u) + 3 lo g_{2} (v)

3 lo g_{7} (u) - 2 lo g_{7} (v)

What is ln(sqrt(3x))-ln(sqrt(x)) ?
The solution to ln(sqrt(3x))-ln(sqrt(x)) is 1/2 ln(3)