I dont Know why there is a number 3 in the formula!!

1.An investment of $1000 is earning 4% interest per annum compunded annually. If the value, *V*, of the investment after *t* years is given by `V=1000(1.04)^t` , then *t*, written as a fuction of *V*, is

if `V=1000(1.04)^t`

then `log V= log(1000(1.04)^(t))` ,

which is `log V= log 1000 + log(1.04)^(t)` (by applying the product law of logarithms) and `log V= 3 + t(log1.04)` , (by applying the power law of logarithms)

Then `log V - 3= t(log1.04)` and `t=(logV-3)/(log1.04)`

The answer is:

`t=(log(V)-3)/(log(1.04))`

Please I need help with the details!! Thanks

### 1 Answer | Add Yours

Starting with `V=1000(1.04)^t` ; write t as a function of V:

`V=1000(1.04)^t` Take the common logarithm of both sides

`logV=log(1000(1.04)^t)`

Rewrite the RHS using the logarithm property `log(AB)=logA+logB`

`logV=log1000+log(1.04)^t`

`log1000=log_(10)1000=3` since `10^3=1000`

Use the logarithm property `log(a)^x=xloga`

`logV=3+tlog(1.4)` Subtract 3 from both sides

`tlog(1.4)=logV-3` Divide by log(1.4)

`t=(logV-3)/(log1.4)`

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