Solve the system of equationsWrite your answers as ordered pairs . If you find more than one solution, list the solutions in order of i

Question

0

5024

2

Solve the system of equations $\begin{align*} y &= \log_2 (2x), <br /> y &= \log_4 x. \end{align*}$ Write your answers as ordered pairs

. If you find more than one solution, list the solutions in order of increasing value of

and separate your answers with semi-colons. So, for example, you would type "(2,2);(4,6)" to say that

and

are the two solutions.

Your Response:

Guest Dec 14, 2014

+23254

+13

Best Answer

Since y = log₂(2x) ---> 2^y = 2x.

Since y = log₄(x) ---> 4^y = x

Since 4 = 2², (2²)^y = x ---> 2^2y = x

Since 2^2y = x ---> 2·2^2y = 2·x ---> 2^2y+1 = 2x = 2^y (from the first equation.

Because 2^2y+1 = 2^y ---> 2y + 1 = y ---> y + 1 = 0 ---> y = -1

Becaue y = -1 and 4^y = x ---> x = 4^-1 ---> x = 1/4

geno3141 Dec 15, 2014

geno3141 · Answer 1 · 2014-12-15T12:47:52