# Logarithms Question

Hey guys, i’m trying to do this logarithm question here:
The value of a sculpture, £V, is modelled by the equation V = Ap^t, where A and p are constants and t is the number of years since the value of the painting was first recorded on 1st January 1960

The line I passes through the point (0,log10(20)) and (50,log10(2000))

b. Using your answer to part a or otherwise, find the values of A and p.

I’ve gotten to the point of equating the 2 equations like this:

1/25 t + log10 20 = t log10 p + log10 A

but i’m not sure how to eliminate the terms to find p and A
Original post by ramell
Hey guys, i’m trying to do this logarithm question here:
The value of a sculpture, £V, is modelled by the equation V = Ap^t, where A and p are constants and t is the number of years since the value of the painting was first recorded on 1st January 1960

The line I passes through the point (0,log10(20)) and (50,log10(2000))

b. Using your answer to part a or otherwise, find the values of A and p.

I’ve gotten to the point of equating the 2 equations like this:

1/25 t + log10 20 = t log10 p + log10 A

but i’m not sure how to eliminate the terms to find p and A

This is not right. I don't know why exactly you have equated two different quantities here.

From $V=A p^t$ we take logs (with respect to base 10) to get $\log V = \log A + t\log p$.

Now use the data you have been provided. When $t=0$ you have $\log V = \log 20$ giving therefore

$\log V = \log A + t\log p \implies \log 20 = \log A$

Whereas when $t=50$ you have $\log V = \log 2000$ therefore

$\log V = \log A + t\log p \implies \log 2000 = \log A + 50 \log p$

So you have two relations $\begin{cases} \log 20 = \log A \\ \log 2000 = \log A + 50 \log p \end{cases}$

Work out A,p from these.
(edited 7 months ago)