SOLUTION: Dear Sir/Madam, Please help me with this math problem. If(logax) (logbx) = logab, find x note: in logax and logbx, a and b are the base. And in logab, a is the base.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Dear Sir/Madam, Please help me with this math problem. If(logax) (logbx) = logab, find x note: in logax and logbx, a and b are the base. And in logab, a is the base.       Log On


   

Question 894845: Dear Sir/Madam,
Please help me with this math problem.
If(logax) (logbx) = logab, find x

note: in logax and logbx, a and b are the base. And in logab, a is the base.
Thank you very much!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%28a%2C%28x%29%29%2Alog%28b%2C%28x%29%29=log%28a%2C%28b%29%29
Convert all logs to log base 10.

+log%2810%2C%28x%29%29%5E2=log%2810%2C%28b%29%29%5E2
+log%2810%2C%28x%29%29=log%2810%2C%28b%29%29 and +log%2810%2C%28x%29%29=-log%2810%2C%28b%29%29
+log%2810%2C%28x%29%29=log%2810%2C%28b%29%29 and +log%2810%2C%28x%29%29=log%2810%2C%281%2Fb%29%29
+x=b and +x=1%2Fb