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Struggling with a logs question. Please help!

"An exponential model may be used for this data, assuming that the relationship between h and t is of the form h = a * 10^bt, where a and b are constants to be determined.

Show that this relationship may be expressed in the form log10h = mt + c, stating the values of m and c in terms of a and b."


I know the answer is the following,

log10h = log10a + bt
m = b, c = log10a

but I'm not sure how to get to it. Please help! :confused:
(edited 9 years ago)
Reply 1
Avatar for hrunting
hrunting
9
if you log both sides of the original equation, the left is log10h, and the right is log10(a*10^bt), and you can split up the right into log10(a)+log10(10^bt) which is equal to log10(a)+bt.
From there, the log10h matches, so you need log10(a)+bt in the form mt+c. Conveniently, it's already in this form, and m=b and c=log10(a).
Original post by hrunting
if you log both sides of the original equation, the left is log10h, and the right is log10(a*10^bt), and you can split up the right into log10(a)+log10(10^bt) which is equal to log10(a)+bt.
From there, the log10h matches, so you need log10(a)+bt in the form mt+c. Conveniently, it's already in this form, and m=b and c=log10(a).


Thank you ever so much! :biggrin:

I am still a little confused though. Why does log10(10^bt) simplify to bt? Is there a log rule I am missing or am I being plain old stupid?

EDIT: GOT IT. Log10(10) = 1, therefore btlog10(10) is simply bt. I'm so embarrassed now.
(edited 9 years ago)

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