How do you solve -3e^(9x-1)+6=-583e9x1+6=58?

1 Answer
Nov 20, 2016

x=1/9(ln(64/3)+1)x=19(ln(643)+1)

Explanation:

-3e^(9x-1)+6=-583e9x1+6=58

Subtract 6 from each side:
-3e^(9x-1)=-643e9x1=64

Divide each side by -3:
e^(9x-1)=64/3e9x1=643

To isolate x, rewrite the equation as a natural log:
9x-1=ln(64/3)9x1=ln(643)

Add 1 to each side:
9x=ln(64/3)+19x=ln(643)+1

Divide each side by 9:
x=1/9(ln(64/3)+1)x=19(ln(643)+1)

This can be expanded and written as:
x=1/9(ln64-ln3+1)x=19(ln64ln3+1)