100=1.5((1.1^(n) - 1))/1.1-1

Could you be so nice please and help me find the solution. The answer is 22 but I have whole time different number. I use log on both sides :

100=1.5((1.1^(n) - 1))/1.1-1
10 = 1.5(1.1^(n) - 1)
10 = 1.65^n - 0.5)
log 10.5 = n log 1.65
n = 0.21321

Thank you so much for huge help:)))

1.5 * 1.1^n is NOT 1.65^n

That's like saying 2*3^2 = 5^2

Also you are saying that
1.5(-1) = .5
The correct algebra is

100=1.5((1.1^(n) - 1))/(1.1-1)
10 = 1.5(1.1^(n) - 1)
Now divide by 1.5
20/3 = 1.1^n - 1
23/3 = 1.1^n
n = log(23/3)/log(1.1) = 21.37
or 22 if you round up to the whole number of payments