SOLUTION: simplify the expression: y=5^log base 5 (2X-14.3) *all of it is the exponent* I don't know what to do since the log in is the exponent- I've never seen this before... please help

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: simplify the expression: y=5^log base 5 (2X-14.3) *all of it is the exponent* I don't know what to do since the log in is the exponent- I've never seen this before... please help      Log On


   

Question 324952: simplify the expression: y=5^log base 5 (2X-14.3) *all of it is the exponent*
I don't know what to do since the log in is the exponent- I've never seen this before... please help!
Found 2 solutions by Fombitz, jessica43:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The important identity here is
a%5E%28log%28a%2C%28x%29%29%29=x since they're inverse functions.
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y=5%5E%28log%285%2C%28%282X-14.3%29%29%29%29
y=2X-14.3

Answer by jessica43(140) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this problem, you are going to need to use the base b logarithm formula to rewrite the problem:
log(base b)a = c means the same as b^c = a
So in this problem:
5^log base 5 (2x-14.3)= y
a = y, b= 5 and c= log base 5 (2x-14.3).
Using the formula, it can be rewritten as:
log(base b)a = c
log (base 5) y = log (base 5) (2x-14.3)
Since it is log (base 5) on each side, they cancel so you end with:
y = 2x-14.3