SOLUTION: log↓2(6x-1)-3=2log↓2(x) I don't even know where to start.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: log↓2(6x-1)-3=2log↓2(x) I don't even know where to start.      Log On


   

Question 1106333: log↓2(6x-1)-3=2log↓2(x)
I don't even know where to start.
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1, explain what the arrows mean.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note you can write "log base 2 of x" as "log(2,x)", or, better yet, "log(2,(x))".

log%282%2C%286x-1%29%29-3+=+2log%282%2C%28x%29%29
log%282%2C%286x-1%29%29-log%282%2C%288%29%29+=+2log%282%2C%28x%29%29 [write the constant 3 as log base 2 of something]
log%282%2C%28%286x-1%29%2F8%29%29+=+log%282%2C%28x%5E2%29%29 [rules of logarithms: difference of logs = log of quotient; log(x^n) = n*log(x)]
%286x-1%29%2F8+=+x%5E2 [if the logs of the expressions are equal, then the expressions are equal]
6x-1+=+8x%5E2
8x%5E2-6x%2B1+=+0
%284x-1%29%282x-1%29+=+0
x+=+1%2F4 or +x+=+1%2F2

Both solutions satisfy the original equation, so both are solutions.