SOLUTION: How do I solve the following logarithm for x? The base of the log is x. log64=3/2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I solve the following logarithm for x? The base of the log is x. log64=3/2      Log On


   

Question 698509: How do I solve the following logarithm for x?
The base of the log is x.
log64=3/2
Found 3 solutions by stanbon, MathLover1, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
Answer by MathLover1(20854) About Me  (Show Source):
You can put this solution on YOUR website!

log%28x%2C64%29=3%2F2....in base ten will be

log%2864%29%2Flog%28x%29=3%2F2...cross multiply

2log%2864%29=3log%28x%29

2log%282%5E6%29=3log%28x%29

2%2A6log%282%29%2F3=log%28x%29

2%2Across%286%292log%282%29%2Fcross%283%29=log%28x%29

2%2A2log%282%29=log%28x%29

4log%282%29=log%28x%29

log%282%5E4%29=log%28x%29

2%5E4=x

16=x



Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve the following logarithm for x?

The base of the log is x.

log64=3/2

Another easy-peasy one!!
log+%28x%2C+%2864%29%29+=+3%2F2
matrix%282%2C1%2C+%22+%22%2C+x%5E%283%2F2%29%29+=+64 ---- Converting to EXPONENTIAL form
matrix%282%2C1%2C+%22+%22%2C+x%5E%28%283%2F2%29%282%2F3%29%29%29+=+64%5E%282%2F3%29 ---- Raising each side to the %282%2F3%29%5E%28rd%29 power 

x%5E1+=+x+=+%28root+%283%2C+64%29%29%5E2+=+4%5E2+=+16