Question

solving logarithmic equation for (x).
Confused.
log*2*(X)=log*2*(x+1)=log*2*12
-number within the * =a, as in the number below the g in log

Answer 1

Well, if you have \[\log_{2}a=\log_{2}b=\log_{2}c \]
then a = b = c.
Are there supposed to be two = signs?

Answer 2

i meant to put an addition sign for the first one

Answer 3

Ok, so...

\[\log_{2}x+\log_{2}(x+1)=\log_{2}12 \]

You use log transformations to turn the sum of two logs into the log of a product:

\[\log_{2}(x^2+x)=\log_{2}12 \]

So, cancel out the logs to get x^2 + x = 12 --> x^2 + x - 12 = 0 --> (x+4)(x - 3) = 0 --> x = 3 or -4. However, the inside of a log cannot be negative, so plug 3 and -4 into the original equation. -4 does not work, so x = 3 is the only answer..

Answer 4

Thanks so much. The last part was the one I had trouble with. Because instead I moved log12 to the other side first making everything = to 0. then i used the law to combine them. But now I understand my fault. I need to pa attention to the square sign as well. Thanks!