Question

solve the equation for x

Answer 1

\[\log _{4}\frac{ 1 }{ 16}=x\]

Answer 2

convert it into index form first.

Answer 3

i got this far \[16^{-1}=4^{x}\]

Answer 4

ok 16^(-1) = 1/16

Answer 5

4^(x) = 1/16
take log both sides

Answer 6

ahh

Answer 7

xln(4) = ln(1/16)

Answer 8

you able to proceed?

Answer 9

\[(16)^{-1}=(4^2)^{-1}=4^{-2}\]

Answer 10

so \[\frac{ \ln1/16 }{ \ln4 }\] ?

Answer 11

now, equate the exponents on both sides

Answer 12

thx

Answer 13

wait @electrokid: why convolute the problem? just (16)^(-1) then use a calculator.

Answer 14

the idea is to convert the "logarithm" form to "exponent" form

Answer 15

i need an exact solution also

Answer 16

you had
\[(16)^{-1}=4^x\\
(4^2)^{-1}=4^x\]
you see?
@uri were you being sarcastic?

Answer 17

electrokid give uri a medal also im gonna give u one...

Answer 18

but, you see, @uri?

Answer 19

this problem does not need a calculator!

Answer 20

yeah lol!
my bad :(
just havent touched logarithms for a while.

Answer 21

so x = -2?

Answer 22

yep

Answer 23

YAAAY!!!

Answer 24

:)