Question

Suppose a house that costs $270,000 appreciates by 5% each year.
In about how many years will the house be worth $350,000? Use the equation 350 = (270)(1.05)x and round the value of x to the nearest year.

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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.