how do you solve f(x)=2^3x+5 and how do you find f^-1 9x) ?

Question

shadowfiend · Answer

Use the log, Luke ;)

Seriously though, when you see a variable in a power, you can use logs to pull it out. Since you're solving, set f(x) = 0 and get:

$$0 = 2^{3x} + 5$$
Now try to see if you can get that into a log form that makes sense.

anonymous · Answer

what do i do after i get 2^3x = -5 ?

anonymous · Answer

?

shadowfiend · Answer

Ok, so remember:

$$a^b = c$$
$$log_a c = b$$

shadowfiend · Answer

Can you apply that above?

anonymous · Answer

i'll try...

shadowfiend · Answer

Hm... Wait... Hehehe. I have detected a problem! That requires the log of a negative number, which does not exist.

anonymous · Answer

?

anonymous · Answer

so what do i do then?

shadowfiend · Answer

Just to double check, the equation is:

$$f(x)=2^{3x}+5$$

Right?

anonymous · Answer

yeah

anonymous · Answer

is that it? shouldn't there be more problem solving?

shadowfiend · Answer

Can your answer have imaginary numbers?

anonymous · Answer

it polly should my math teacher loves i

shadowfiend · Answer

Hahaha. Well, the log of -5 is 0.698970004 + 1.36437635 i
 :p

anonymous · Answer

ow and wow OK

shadowfiend · Answer

Hehe. Yeah it's kind of nasty. If it were 2^(3x) - 5 instead of + 5 things would be a lot better.

anonymous · Answer

thanx though--- awesome response math wizard (:

shadowfiend · Answer

Oh that's not me. Amistre's not here at the moment but he's the wizard around here ;)

anonymous · Answer

oh, wait how is the second part done?

anonymous · Answer

f ^-1 (x)?

shadowfiend · Answer

Post that as a separate question. I'm a bit rusty on function inverses :)

anonymous · Answer

k