Question

Express 5t in terms of the base 2 exponential function

Answer 1

\[f(t)=5^t\] like that?

Answer 2

and you want to use the base \(2\) rather than \(5\) ?

Answer 3

yes

Answer 4

only thing i can think of is to solve \[5^x=2\] for \(x\)

Answer 5

by the change of base formula you get
\[x=\frac{\ln(2)}{\ln(5)}\] making
\[\large 5^{\frac{\ln(2)}{\ln(5)}}=2\] and so
\[\left(\large 5^{\frac{\ln(2)}{\ln(5)}}\right)^t=2^t\]

Answer 6

oh but maybe that is backwards!

Answer 7

yes, it is backwards i think
solve \[2^x=5\] so
\[x=\frac{\ln(5)}{\ln(2)}\]etc etc

Answer 8

was thinkinking the same, i am pretty confused...i hate it when math problems are worded, but thanks

Answer 9

yeah, it is confusing but i think what you want is \[\left(\large 2^{\frac{\ln(5)}{\ln(2)}}\right)^t=5^t\]