What is 3ln|x-3|+5ln|x+2|+5/9 ln|2x+3| ?

The solution to 3ln|x-3|+5ln|x+2|+5/9 ln|2x+3| is ln(|x-3|^3|x+2|^5|2x+3|^{5/9})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3ln|x-3|+5ln|x+2|+5/9 ln|2x+3|

simplify

3 ln ∣ x - 3 ∣ + 5 ln ∣ x + 2 ∣ + \frac{5}{9} ln ∣ 2 x + 3 ∣

ln (∣ x - 3 ∣^{3} ∣ x + 2 ∣^{5} ∣ 2 x + 3 ∣^{\frac{5}{9}})

Solution steps

3 ln ∣ x - 3 ∣ + 5 ln ∣ x + 2 ∣ + \frac{5}{9} ln ∣ 2 x + 3 ∣

Apply log rule:

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

3 ln ∣ x - 3 ∣ = ln (∣ x - 3 ∣^{3})

= ln (∣ x - 3 ∣^{3}) + 5 ln ∣ x + 2 ∣ + \frac{5}{9} ln ∣ 2 x + 3 ∣

Apply log rule:

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

5 ln ∣ x + 2 ∣ = ln (∣ x + 2 ∣^{5})

= ln (∣ x - 3 ∣^{3}) + ln (∣ x + 2 ∣^{5}) + \frac{5}{9} ln ∣ 2 x + 3 ∣

Apply log rule:

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

ln (∣ x - 3 ∣^{3}) + ln (∣ x + 2 ∣^{5}) = ln (∣ x + 2 ∣^{5} ∣ x - 3 ∣^{3})

= ln (∣ x - 3 ∣^{3} ∣ x + 2 ∣^{5}) + \frac{5}{9} ln ∣ 2 x + 3 ∣

Apply log rule:

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

\frac{5}{9} ln ∣ 2 x + 3 ∣ = ln (∣ 2 x + 3 ∣^{\frac{5}{9}})

= ln (∣ x + 2 ∣^{5} ∣ x - 3 ∣^{3}) + ln (∣ 2 x + 3 ∣^{\frac{5}{9}})

Apply log rule:

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

ln (∣ x + 2 ∣^{5} ∣ x - 3 ∣^{3}) + ln (∣ 2 x + 3 ∣^{\frac{5}{9}}) = ln (∣ x + 2 ∣^{5} ∣ x - 3 ∣^{3} ∣ 2 x + 3 ∣^{\frac{5}{9}})

= ln (∣ x - 3 ∣^{3} ∣ x + 2 ∣^{5} ∣ 2 x + 3 ∣^{\frac{5}{9}})

lo g_{10} (a) + 4 lo g_{10} (b) - 2 lo g_{10} (c)

lo g_{10} (\frac{a}{b ^{2}})

lo g_{10} (\frac{( x ^{x} )}{5})

lo g_{2} (\frac{x}{y})

ln (\frac{x ^{6}}{x ^{2} - 25})

What is 3ln|x-3|+5ln|x+2|+5/9 ln|2x+3| ?
The solution to 3ln|x-3|+5ln|x+2|+5/9 ln|2x+3| is ln(|x-3|^3|x+2|^5|2x+3|^{5/9})