SOLUTION: Alright, the question is log base 3 2x+log base 3 7= log base 3 28. I know that the answer is 2, but i have no clue how to get to it. I tried canceling out the log base 3 part

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Alright, the question is log base 3 2x+log base 3 7= log base 3 28. I know that the answer is 2, but i have no clue how to get to it. I tried canceling out the log base 3 part      Log On


   

Question 493072: Alright, the question is log base 3 2x+log base 3 7= log base 3 28.

I know that the answer is 2, but i have no clue how to get to it. I tried canceling out the log base 3 part since they are all the same, and then it came out to 2x+7=28 and solved that, but then x would equal 10.5z please help!
Found 3 solutions by nerdybill, josmiceli, Gogonati:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
apply "log rules":
log%283%2C2x%29+%2B+log%283%2C7%29+=+log%283%2C28%29
log%283%2C%282x%29%287%29%29+=+log%283%2C28%29
log%283%2C14x%29+=+log%283%2C28%29
+14x+=+28
+x+=+2

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula
+log%28+a%2Ab+%29+=+log%28a%29+%2B+log%28b%29+ ( in reverse )
+log%283%2C2x%29+%2B+log%283%2C7%29+=+log%283%2C28%29+
+log%283%2C2x%2A7%29+=+log%283%2C28%29+
If the logs are equal, the numbers are equal
( the base could be anything you want )
+14x+=+28+
+x+=+2+

Answer by Gogonati(855) About Me  (Show Source):