.89=.76(1.04)^x

First get rid of the .76 on the RHS (right hand side)

(.89/.76) = 1.04^x

Now lets take the natural log of each side

ln (.89/.76) = ln 1.04^x

Now lets use our log/ln rules for the RHS

ln (.89/.76) = x (ln 1.04)

Now just divide on the RHS and you found the exact value of x

x = [ ln (.89/.76) / ln (1.04) ]