What is 1/2 ln(x-3)+1/2 ln(x+3)-ln(x) ?

The solution to 1/2 ln(x-3)+1/2 ln(x+3)-ln(x) is ln(((x-3)^{1/2}(x+3)^{1/2})/x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 ln(x-3)+1/2 ln(x+3)-ln(x)

simplify

\frac{1}{2} ln (x - 3) + \frac{1}{2} ln (x + 3) - ln (x)

ln (\frac{( x - 3 ) ^{\frac{1}{2}} ( x + 3 ) ^{\frac{1}{2}}}{x})

Solution steps

\frac{1}{2} ln (x - 3) + \frac{1}{2} ln (x + 3) - ln (x)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

4.74 + lo g_{10} (\frac{50}{10})

\frac{( ln ∣ x + 4 ∣ - 6 ln ∣ x - 1 ∣ )}{5}

- ln (\frac{x + 1}{e ^{x}})

ln (- 1 e^{- x})

What is 1/2 ln(x-3)+1/2 ln(x+3)-ln(x) ?
The solution to 1/2 ln(x-3)+1/2 ln(x+3)-ln(x) is ln(((x-3)^{1/2}(x+3)^{1/2})/x)