3^(x+2)=5^x

3^(x+2)=5^x

Taking the log of both sides, we have

log3^(x+2)= log5^x    and b a property of logs, we can write

(x+2) log 3 = x log 5     simplify

x log 3   + 2 log 3  = x log 5      rearrange

2 log 3  = x log 5 - x log 3          factor on the right

2 log 3 = x (log 5 - log 3)           divide both sides by  (log 5 - log 3)

(2 log 3) / (log 5 - log 3)  = x =  about 4.3013