Question

simplify e^(-3ln1/2)

Answer 1

Well, what is
\[ e^{\ln a} = ... \]

Answer 2

\[ e^{\ln a} = a \] yes. Now what's, \( -3 \ln(1/2) \) equal to?

Answer 3

\[ a \ln x = \ln x^a \]

Answer 4

Hence
\[ -3 \ln 1/2 = \ln (1/2)^3 \]

Answer 5

**correction
\[ -3 \ln 1/2 = \ln(1/2)^{-3} = \ln 2^3 \]

Answer 6

Now see what to do?

Answer 7

ranstucker, write your answers here, not in private message to me

Answer 8

3ln2

Answer 9

you could do that, but we want
\[ e^{-3 \ln(1/2) } \]
so it is useful to write -3 ln (1/2) as just ln(x) for some x, because then
\[ e^{-3 \ln(1/2)} = e^{ln x} = x \]

Answer 10

so what is the answer?

Answer 11

well, if
\[ -3 \ln (1/2) = \ln x \]
what is x equal to?

Answer 12

scroll up, we already calculated this

Answer 13

I've got to get to class

Answer 14

bye then