"Consider the infinite geometric series

1 + (2x/3) + (2x/3)^2 + (2x/3) ^3 +...

For what values of x does the series converge?"

I know convergence means the sum tends to a finite series, so I have used the equation Sn = u/(1-r) where u = first term and r = ratio

Sn = 1/(1-2x/3)

But then I have no idea what to do next. I know (1- 2x/3) cannot be 0.

Second question is

"Solve 2(5^(x+1)) = 1 + 3/(5^x), giving the answer in the form a + log(base 5) b, where a and b are integers"

I managed to solve for x, but I have no idea how to put it in the form a + log(base 5) b

I got to 5^x = 3/5 or 5^x = -0.5

so x would just be the log (base 5) 3/5 (because it can't be negative)

Thanks for your time and effort