House loses value each year. How long will it take for the house to be worth $150000

Question

A house purchased for $\$226000$ loses $4\%$ of its value each year. How long will it take for the house to be worth $\$150000$?

The way I set up the equation was $150000=(226000)(.96)^x$. I just wasn't sure that was right.

Answer 1

$150000=226000(0.96)^t$

Now divide both sides by $226000$.

$0.6673=(0.96)^t$

The next step is this:

$t = \dfrac{\log 0.6673}{\log 0.96} \approx 10$ years

I hope this helps! Just remember that if $a=b^x$ then $x= \dfrac{\log a}{\log b}$.