What is ln(r^9s^{53}sqrt(r)5s^2) ?

The solution to ln(r^9s^{53}sqrt(r)5s^2) is 9ln(r)+ln(sqrt(r))+ln(5)+55ln(s)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(r^9s^{53}sqrt(r)5s^2)

simplify

ln (r^{9} s^{53} r 5 s^{2})

9 ln (r) + ln (r) + ln (5) + 55 ln (s)

Solution steps

ln (r^{9} s^{53} r \cdot 5 s^{2})

Apply log rule:

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

ln (r^{9} s^{53} r \cdot 5 s^{2}) = ln (r^{9}) + ln (s^{53}) + ln (r) + ln (5) + ln (s^{2})

= ln (r^{9}) + ln (s^{53}) + ln (r) + ln (5) + ln (s^{2})

Apply log rule:

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

ln (r^{9}) = 9 ln (r)

= 9 ln (r) + ln (s^{53}) + ln (r) + ln (5) + ln (s^{2})

Apply log rule:

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

ln (s^{53}) = 53 ln (s)

= 9 ln (r) + 53 ln (s) + ln (r) + ln (5) + ln (s^{2})

Apply log rule:

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

ln (s^{2}) = 2 ln (s)

= 9 ln (r) + 53 ln (s) + ln (r) + ln (5) + 2 ln (s)

Group like terms

= 9 ln (r) + ln (r) + ln (5) + 53 ln (s) + 2 ln (s)

Add similar elements:

53 ln (s) + 2 ln (s) = 55 ln (s)

= 9 ln (r) + ln (r) + ln (5) + 55 ln (s)

0.000003 ln (\frac{100}{5200})

lo g_{10} (4 \cdot 1 0^{- 8})

9 ln (18) - 5 ln (10)

- ln (e^{x} + 1) + ln (2)

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

What is ln(r^9s^{53}sqrt(r)5s^2) ?
The solution to ln(r^9s^{53}sqrt(r)5s^2) is 9ln(r)+ln(sqrt(r))+ln(5)+55ln(s)