Can someone help me to solve these questions please?

1) 3^x+1=9^x. Find the value of x.

2) find the value of m for which.
3^2M^-1=243.

since 9 = 3^2, 9^x = 3^2x

So, you have

3^(x+1) = 3^(2x)
x+1 = 2x
x = 1

On the other one, I will guess you mean

3^2 * m^-1 = 243
m^-1 = 27
m = 1/27