Stuck finding out the manual solution for finding x in this logarithmic equation

Submitted by Je Gonzaga on

Good day,

I got stuck finding the manual solution for this problem without relying to the solve function of Casio calculator

The original equation was

[(1+x)40] -1 = (181205.95/3000)x

Then I tried using properties of logarithm and I simplified it to this equation:

[ln(181205.95/3000)]/40 = ln(1+x) - (1/40)[ln(x+3000/181205.95)]

0.102526 = ln(x+1) - 0.025ln(x+0.0165557)

Answer: x = 0.02

I was trying to just use properties of logarithms to solve this but if you have other solutions, I'll gladly study that.

and this:

1.1881 = (1+0.18/x)^x

Maraming salamat po :D