Question

How do you solve this? log 2 x + log x (x+2) = log 2 (x + 6)

Answer 1

http://www.teachengineering.org/collection/van_/lessons/van_bmd_less2/log_properties_lesson2_fig2.jpg

Answer 2

Does the question really look like\[\log _2 x + \log _2 (x+2) = \log_2 (x + 6)\]?

Answer 3

that is the equation

Answer 4

Would it be the equality property?

Answer 5

Assuming it does, work it like this\[\log_2 x + \log_2 (x+2) = \log_2 (x + 6) \implies \log_2(x^2+2x)=\log_2(x+6)\]\[\implies x^2+2x=x+6 \implies x^2+x-6=0 \implies (x+3)(x-2)=0\]\[\implies x=2\]Note that the second solution of the quadratic equation (x=-3) is not in the domain of the problem.

Answer 6

Is that because a negative number can't ever be in the domain of the problem?

Answer 7

The first term of the problem is log base 2 of x. Can't take the log of a non-positive number.

Answer 8

Ohhh

Answer 9

Thanks for helping :)

Answer 10

Justifications for the steps, in order, are: Product rule, characteristics of one-to-one functions, addition rule for equations, factorization properties, zero product property, and domain rules for logs (to discard the negative solution).

Answer 11

No sweat. Do math every day.