How do you expand #ln(x(x+11))^3#?

1 Answer
Feb 9, 2016

Answer:

#ln( x(x+11) )^3 = 3 ln(x) + 3 ln(x+1)#

Explanation:

You can use the following two logarithmic laws:

[1] #" " log_a(m * n) = log_a(m) + log_a(n)#

[2] #" " log_a(m ^r) = r * log_a(m)#

So, let's transform your term:

#ln( x(x+11) )^3 stackrel("[2] ")(=) 3 * ln(x(x+1))#

#stackrel("[1] ")(=) 3 ( ln(x) + ln(x+1))#

#= 3 ln(x) + 3 ln(x+1)#

From here on, you can't expand this expression any further.