Question

log2 (-13.4) PLEASE HELP

Answer 1

\[\log_{2}(-13.4) \]

Answer 2

i only know how to take the ln of negative numbers based on euler's formula

Answer 3

because \[e^{\pi*i} = -1\]

Answer 4

@jim_thompson5910 can you help me please?

Answer 5

let's see how far we get using that equation

Answer 6

\[\Large e^{\pi*i} = -1\]
\[\Large 13.4*e^{\pi*i} = 13.4*(-1)\]
\[\Large 13.4*e^{\pi*i} = -13.4\]

see where I'm going with this?

Answer 7

okay this makes sense. but how will i take \[\log_{2} \] and clear e?

Answer 8

by using the change of base formula

\[\Large \log_{b}(x) = \frac{\ln(x)}{\ln(b)}\]

Answer 9

the logs on the right side can be any base you want, in this case, they are base e

Answer 10

just make sure that the logs on the right side have the same base

Answer 11

so then would i say:\[\log_{2}(-13.4) = \frac{ \ln (-13.4) }{ \ln (2) } \] \[\frac{ \ln (-1) * \ln(13.4) }{ \ln(2) }\] \[\frac{ i \pi * \ln(13.4) }{ \ln(2) }\]

and that would be my answer when i put the two natural logs in my calculator?

Answer 12

close

Answer 13

but you use the rule log(x*y) = log(x)+log(y)

Answer 14

that means ln(-1*13.4) = ln(-1) + ln(13.4) = pi*i + ln(13.4)

Answer 15

oh okay thank you very much!

Answer 16

you're welcome