Question

Solve the equation. Give an exact solution.
log4(x-6)+log4(x-6)=1
A)8
B)37
C)-37,37
D)-8,8

Answer 1

c is square root -37 and 37

Answer 2

You mean \(log_4(x-6)\) right? I mean base of log is 4, right?

Answer 3

yea

Answer 4

I got A)

Answer 5

how is the process though? i dont know what formula to use

Answer 6

Since you have options, then use it.
Try x =8, then \(log_4( 8-6) = log_4(2)\)
so the left hand side is \(log_4(2) + log_4(2) = 2log_4(2) = log_4(2^2)=log_44=1\)

Answer 7

If you need formula, then use this:
\(log_a b + log_a c= log_a (b*c)\)

Answer 8

much obliged

Answer 9

Since your 2 terms are the same, (the formula still hold)

Answer 10

you just apply it.

Answer 11

another way by using the convenience of the same term:
\(log_4(x-6) + log_4(x-6) =2log_4(x-6) =log_4(x-6)^2=1\)
and you know that \(1= log_44\)
hence \(log_4(x-6)^2=log_44\), that allows you conclude that
\((x-6)^2= 4\\x-6=\pm2\),
hence x = 8 or x =4 .
We reject x =4 because it makes \(log_4(x-6) = log_4(-2)\) which is undefined.

Answer 12

So far, I gave you 3 way to get the answer, right? hehehe..