**Given that:**

2logan = loga18 + loga ( n - 4 )

find the possible values of n.

>>how do i get to __logan^2 = loga 18(n-4)__

is it correct that

2logan = 2 logan^2

how do you get from:

**loga18 + loga ( n - 4 )**

to **logan^2 = loga 18(n-4)**

(Nerd)(Nerd)

I assume you mean base a.

\(\displaystyle 2\log_a(n) = \log_a(n^2)\) is true as it's the power law.

You can simplify the RHS using the addition law:

\(\displaystyle \log_a(18) + \log_a(n-4) = \log_a[18(n-4)]\)

\(\displaystyle \log_a(n^2) = \log_a[18(n-4)]\)

Now if the two bases are the same then the exponents must be equal.

\(\displaystyle n^2 = 18(n-4)\)

Which is a standard quadratic equation but remember that \(\displaystyle n>0\) to satisfy the original domain