Question

Which of the following is a solution to the equation log 4 x + log 4 (x – 3) = 1 ?

Answer 1

\[\log_a b + \log_a c=\log_abc\]so\[\log_4(x(x-3))=1\]\[4^1=x(x-3)\]nowsolve for x

Answer 2

use the log laws for the left hand side

\[\log _{4} x + \log _{4} (x - 3) = \log _{4} (x^2 - 3x)\]

raise to a power of 4

\[x^2 - 3x = 4^1\]

gives x^2 - 3x - 4 = 0

(x - 4)(x+1)= 0

then x = 4 or -1