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

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Answer 1 · 2016-02-09T14:14:36

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

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.

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