SOLUTION: I am checking my answer to expand my expression: log3(3square root x /81) I get: 1/3log3 x-4 Did I do this correctly?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am checking my answer to expand my expression: log3(3square root x /81) I get: 1/3log3 x-4 Did I do this correctly?      Log On


   

Question 687625: I am checking my answer to expand my expression:
log3(3square root x /81)
I get:
1/3log3 x-4
Did I do this correctly?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Is this correct:
+log%28+3%2C+%28+3%2Asqrt%28x%2F81%29+%29%29+ ?, if so
+log%28+3%2C3+%29+%2B+log%28+3%2C+%28x%2F81%29%5E%281%2F2%29+%29+
+1+%2B+%281%2F2%29%2Alog%28+3%2C%28x%2F81%29+%29+
+1+%2B+%281%2F2%29%2A%28+log%28+3%2C+x+%29++-+log%28+3%2C81+%29+%29+
+1+%2B+%281%2F2%29%2A%28+log%28+3%2Cx+%29+-+4+%29+
+%281%2F2%29%2Alog%28+3%2C+x+%29+-+2+%2B+1+
+%281%2F2%29%2Alog%28+3%2Cx+%29+-+1+ answer
check:
+log%28+3%2C+%28+3%2Asqrt%28x%2F81%29+%29%29+=+%28+1%2F2+%29%2Alog%28+3%2Cx+%29+-+1+
Multiply both sides by +2+
+2%2Alog%28+3%2C+%28+3%2Asqrt%28x%2F81%29+%29%29+=+log%28+3%2Cx+%29+-+2+
+log%28+3%2C+9%2A%28x%2F81%29+%29+=+log%28+3%2Cx+%29+-+2+
+log%28+3%2C+x%2F9+%29+=+log%28+3%2Cx+%29+-+2+
+log%28+3%2Cx+%29+-+log%28+3%2C9+%29+=+log%28+3%2Cx+%29+-+2+
+log%28+3%2Cx+%29+-+2+=+log%28+3%2Cx+%29+-+2+
OK
Unless I goofed- check it carefully