How do you solve e18x=7957?

2 Answers
Nov 16, 2016

Using the inverse function ln we convert it to a simple algebraic expression.

Explanation:

Using the inverse function ln we convert it to a simple algebraic expression.
ln(e18x=ln(7957) (look up ln(7957) or use a calculator)

1-8x = 8.98 ; -8x = 7.98 ; x = -0.9975

CHECK:
e180.9975=(7957)
e1+7.98=(7957)
e8.98=(7957) ; 7942 = 7957 (within error of approximation for 2 significant digits)

Nov 16, 2016

e18x=7957 : Given

lne18x=ln7957 : Take the natural log of both sides to try to get a step closer to isolating x

(18x)lne=ln7957 : ln e are inverses of each other, which equals 1. Bring the exponent (18x) to the front.

18x=ln7957

8x=ln79571 : Subtract 1 to the other side to isolate x

x=ln795718 : Divide by 8 to the other side to isolate x