SOLUTION: If, (b/a)^n=a, then what is the answer to (b/a)^x=b

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If, (b/a)^n=a, then what is the answer to (b/a)^x=b      Log On


   

Question 1105705: If, (b/a)^n=a, then what is the answer to (b/a)^x=b
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
if +%28b%2Fa%29%5En+=+a+
and +%28b%2Fa%29%5Ex+=+b+
then +highlight%28x+=+n%2B1%29+
————
Check:
+%28b%2Fa%29%5E%28n%2B1%29+=+%28b%2Fa%29%5En+%2A+%28b%2Fa%29+=+a%28b%2Fa%29+=+b+
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EDIT 1/2/18, to the student:
I will get you started, and you should strive to figure out how I got to the solution on your own.
There may be a more efficient way to solve… this is just how I did it:
+%28b%2Fa%29%5En+=+a+ —> +b+=+a%5E%281%2B1%2Fn%29+ (by taking nth root of both sides, then mult by 'a' on both sides)
Now starting with
+%28b%2Fa%29%5Ex+=+b+
Substitute for 'b'
+%28a%5E%281%2B1%2Fn%29+%2F+a%29%5Ex+=+a%5E%281%2B1%2Fn%29+
+%28a%5E%281%2Fn%29%29%5Ex+=+a%5E%281%2B1%2Fn%29+
Take log() of both sides:
+x+%2A+log%28%28a%5E%281%2Fn%29%29%29+=++%281%2B1%2Fn%29log%28%28a%29%29+

so x = n + 1