The number of years, n, for a piece of machinery to depreciate to a known salvage value can be found using the formula n=(log s-log i)/log (1-d)
where s is the salvage value of the machinery, i is its initial value, and d is the annual rate of depreciation.
b) How many years will it take for a piece of machinery to loose half of its value if the annual rate of depreciation is 15%.

Question

The number of years, n, for a piece of machinery to depreciate to a known salvage value can be found using the formula n=(log s-log i)/log (1-d)
where s is the salvage value of the machinery, i is its initial value, and d is the annual rate of depreciation.
b) How many years will it take for a piece of machinery to loose half of its value if the annual rate of depreciation is 15%.

anonymous · Answer

oh wow i just noticed now on how to do it, the numerator is an identity. $$n=\frac{ \log \frac{ 0.5x }{ x } }{ \log 0.85 }$$

anonymous · Answer

okay so can i now cancel out log to the base 10?

ganeshie8 · Answer

nope thats not allowed, log is a function. not a factor

anonymous · Answer

okay

ganeshie8 · Answer

you're allowed to cancel x inside the log though

anonymous · Answer

oh right

anonymous · Answer

$$n=\frac{ \log 0.5 }{ \log 0.85}$$

anonymous · Answer

wow that was so easy lol. I was struggling with this for half an hour. Anyways thanks for redirecting me to the right track.

ganeshie8 · Answer

so how many years it is ?

anonymous · Answer

4.265 years

ganeshie8 · Answer

yes wolfram says d same http://www.wolframalpha.com/input/?i=ln%280.5%29%2Fln%280.85%29

anonymous · Answer

Okay thanks for the help again :)