Question

Solve for t using logarithms with base a

Answer 1

\[\frac{ A-D }{ B }=a^Ct\]

Answer 2

oh snap the t should also be an exponent

Answer 3

\[\frac{ A-D }{ B }=a ^{ct}\]

Answer 4

\[\frac{ A-D }{ B }=a^{Ct}\]
taking the log to base \(a\) on both sides
\[\log_a\frac{ A-D }{ B }=\log_aa^{Ct}\]

now use \(\boxed{\log_bb^n = n\log_bb = n}\)

Answer 5

you take the log of both sides?

Answer 6

so the right side would be ct?

Answer 7

yepp

Answer 8

Now, to solve for \(t\), divide by \(C\)

Answer 9

\[\frac{ 1 }{ c }\log_{a} \frac{ A-D }{ B }=t\]

Answer 10

good work

Answer 11

:D thank you so much