solve the equation 15^x+1 = 29?

take ln or log both sides
i will take ln so

ln15^x+1=ln29

using ln & log properties the power will be multiplied

x+1(ln15)=ln29
x=[(ln29)/(ln15)]-1 =0.243

Do you mean :-
15^(x + 1) = 29 ????
OR
(15^x) + 1 = 29 ?????

AS WRITTEN it MUST be taken as :-
(15^x) + 1 = 29
15^x = 28
x log 15 = log 28
x = log 28 / log 15
x = 1.23

15^(x + 1) = 29
log[15^(x + 1)] = log[29]
(x + 1)log(15) = log(29)
xlog(5) + log(5) = log(29)
xlog(5) = log(29) - log(5)
xlog(5) = log(29/5)
x = log(29/5)/log(5)

15^x=28x
x=ln(28)/ln(5)
x=1.23