SOLUTION: Exponential equation without using logs. Solve for x: 5^(-3x+1)=15625

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Exponential equation without using logs. Solve for x: 5^(-3x+1)=15625      Log On


   

Question 106642: Exponential equation without using logs. Solve for x:
5^(-3x+1)=15625
Found 2 solutions by edjones, Earlsdon:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
5^(-3x+1)=15625
5^(-3x+1)=5^6 convert to the same base 5
-3x+1=6 use exponents only
-3x=6-1
-3x=5
x=-5/3
Ed

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
5%5E%28-3x%2B1%29+=+15625
Hint: Since you are not permitted to use logarithms, see if 15625 is a power of 5. Yes it is! 15625+=+5%5E6
5%5E%28-3x%2B1%29+=+5%5E6
Now use the fact that:
If x%5En+=+x%5Em then n = m.
-3x%2B1+=+6 Subtract 1 from both sides.
-3x+=+5 Divide both sides by -3.
x+=+-5%2F3