What is ln(5)+3ln(x)+6ln(x^2+9) ?

The solution to ln(5)+3ln(x)+6ln(x^2+9) is ln(5x^3(x^2+9)^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(5)+3ln(x)+6ln(x^2+9)

simplify

ln (5) + 3 ln (x) + 6 ln (x^{2} + 9)

ln (5 x^{3} (x^{2} + 9)^{6})

Solution steps

ln (5) + 3 ln (x) + 6 ln (x^{2} + 9)

Apply log rule:

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

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

= ln (5) + ln (x^{3}) + 6 ln (x^{2} + 9)

Apply log rule:

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

ln (5) + ln (x^{3}) = ln (5 x^{3})

= ln (5 x^{3}) + 6 ln (x^{2} + 9)

Apply log rule:

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

6 ln (x^{2} + 9) = ln ((x^{2} + 9)^{6})

= ln (5 x^{3}) + ln ((x^{2} + 9)^{6})

Apply log rule:

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

ln (5 x^{3}) + ln ((x^{2} + 9)^{6}) = ln (5 x^{3} (x^{2} + 9)^{6})

= ln (5 x^{3} (x^{2} + 9)^{6})

ln (4 e^{\frac{2 π x}{3}})

ln (\frac{1073.15}{273.15})

ln (121) - ln (100)

ln (\frac{19.44}{12.62})

- lo g_{2} (\frac{1}{20})

What is ln(5)+3ln(x)+6ln(x^2+9) ?
The solution to ln(5)+3ln(x)+6ln(x^2+9) is ln(5x^3(x^2+9)^6)