Question

Suppose a house that costs $270,000 appreciates by 5% each year.

Answer 1

Please use " ^ " to indicate exponentiaton:   Use the equation

350 = (270)(1.05)^x.  
Take the log of both sides:

log 350 = log 270 + x*log 1.05.

Subtr. log 270 from both sides:

log 350 - log 270 = x*log 1.05
                               log 350 - log 270
Sove for x:      x = -------------------------
                                  log 1.05
                                                           2.544- 2.431
Evaluate this using a calculator.  x = ------------------
                                                                0.0212

x is then approx. 5.33, or 5 1/3 years.