250^(x+1)=14^(2*x-1) Solve using logarthims
x=-33.5345950817........
Solve for x over the real numbers:
250^(x+1) = 14^(2 x-1)
Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(250) (x+1) = log(14) (2 x-1)
Expand out terms of the left hand side:
log(250) x+log(250) = log(14) (2 x-1)
Expand out terms of the right hand side:
log(250) x+log(250) = 2 log(14) x-log(14)
Subtract 2 x log(14)+log(250) from both sides:
(log(250)-2 log(14)) x = -log(14)-log(250)
Divide both sides by log(250)-2 log(14):
Answer: |
| x = (-log(14)-log(250))/(log(250)-2 log(14))
