Question

1/√8 = 4^(m + 3)

Answer 1

First, why don't we rationalize the denominator of the left-hand side?

Answer 2

1/8^1/2?

Answer 3

Might want to add parenthesis on that :)

Answer 4

1/8^(1/2)

Answer 5

Okay.

Answer 6

Try to move all those square root signs to the top :)

Answer 7

oh, ok, so its 1 = 4√8^(m + 3)?

Answer 8

\(\large \frac{1}{\sqrt{8}}=\frac{1*\sqrt{8}}{\sqrt{8}*\sqrt{8}}=\frac{2\sqrt{2}}{8}=\frac{\sqrt2}{4}\)

Answer 9

That's the left hand side :)

Answer 10

then what would we do for the right?

Answer 11

Well, it begins with taking a logarithm.

Answer 12

write both of them in powers of 2.
i dont think rationalisation is required.
\[1/\sqrt8=2^{-3/2} and 4^{m+3}=2^{2m+6}\]
now equate the powers to find m

Answer 13

vamgadu is probably right - I'm usually too lazy to do the problem the fast way if it is precalculus :P

Answer 14

m = -3?

Answer 15

No.

Answer 16

wait. er

Answer 17

that says 4^m + 3 = 2^2m + 6 right?

Answer 18

OH WAIT NVM. K I GOT IT

Answer 19

Okay, good.

Answer 20

thanks :D