Question

5^(-T/2)=.20
I know the answer, but HOW does one arrive there? What rules are in play here?

Answer 1

@Gralwyn

Answer 2

helps to notice that 0.2=1/5, so you can rewrite
5^(-T/2)=1/5
now take the log base 5 of both sides

Answer 3

how does one do that correctly?

Answer 4

do you know about logarithms?

Answer 5

\[5^{\frac{ -T }{ 2 }}=0.20=\frac{ 20 }{100 }=\frac{ 1 }{5 }=5^{-1}\]
\[\frac{ -T }{2 }=-1,T=?\]

Answer 6

Yes, but I was under the assumption that I could take the log of just one side so
\[(-T/2)\log5{.20}\]

Answer 7

5 is supposed to be the base there.

Answer 8

you cannot "just take the log of one side"\[x=y\neq\log x\]

Answer 9

ok, so log5(-T/2)=log5?

Answer 10

T=-1*-2=2