What is ln(5)+ln(5^2)+ln(5^3) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(5)+ln(5^2)+ln(5^3)

simplify

ln (5) + ln (5^{2}) + ln (5^{3})

6 ln (5)

Decimal Notation

9.65662 \dots

Solution steps

ln (5) + ln (5^{2}) + ln (5^{3})

Apply log rule:

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

ln (5^{2}) + ln (5^{3}) = ln (5^{3} \cdot 5^{2})

= ln (5) + ln (5^{3} \cdot 5^{2})

5^{2} \cdot 5^{3} = 3125

= ln (5) + ln (3125)

ln (3125) = 5 ln (5)

= ln (5) + 5 ln (5)

Add similar elements:

ln (5) + 5 ln (5) = 6 ln (5)

= 6 ln (5)

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

ln (x^{2}) - ln (y^{2})

lo g_{2} ((3^{6} \cdot 7)^{6})

ln (sin (x) cos (x))

lo g_{8} ((x - 5)^{6} (x + 7)^{2})