Question

solve for x
ln(8x-1)=2

Answer 1

ln(8x -1) = 2
8x -1 = e^2
8x = e^2 +1
Divide by 8

x = 1/8(e^2 + 1)

Answer 2

log(8 x-1) = 2
Cancel logarithms by taking exp of both sides:
8 x-1 = e^2
Add 1 to both sides:
8 x = 1+e^2
Divide both sides by 8:
x = 1/8 (1+e^2)
Now test that this solution is appropriate by substitution into the original equation:
Check the solution x = 1/8 (1+e^2):
log(8 x-1) => log(-1+8/8 (1+e^2)) = 2
So the solution is correct.
Thus, the solution is:
x = 1/8 (1+e^2)