1. ## logarithm/exponential word problem

The value V of a certain automobile that is t years old can be modeled by
$\displaystyle V(t)=14,044(0.8)^t$.
According to the model, when will the car be worth:
(a) $8000? (b)$7000?
(c) $1000? Answers: (a) 2.5 years (b) 3.1 years (c) 11.8 years It says I need to rewrite the problem in logarithmic form, how would I do this?$\displaystyle log 8000 = log 14044(.8)^t$? 2. Originally Posted by desiderius1 The value V of a certain automobile that is t years old can be modeled by$\displaystyle V(t)=14,044(0.8)^t$. According to the model, when will the car be worth: (a)$8000?
(b) $7000? (c)$1000?

(a) 2.5 years
(b) 3.1 years
(c) 11.8 years

It says I need to rewrite the problem in logarithmic form, how would I do this?
$\displaystyle log 8000 = log 14044(.8)^t$?

For log form I would suggest this as a function for making t the subject

$\displaystyle V=14044(0.8)^t$

$\displaystyle \frac{V}{14044}= (0.8)^t$

$\displaystyle \log_{0.8}\frac{V}{14044}= t$

$\displaystyle t= \log_{0.8}\frac{V}{14044}$