Question

solve. logx(27)=-3/2

Answer 1

change to exponential form

Answer 2

i don't understand how to do that.

Answer 3

3^3=27

Answer 4

\[\large x^{-\frac{3}{2}} = 27\]

Answer 5

raise both sides by -1

Answer 6

to cancel the negative exponent of x

Answer 7

still there?

Answer 8

yes...trying to work it out and get a grasp on it.

Answer 9

i don't understand. i am getting x=1/9

Answer 10

remember... \[\LARGE x^{\frac{m}{n}} = \sqrt[n]{x^m}\]

Answer 11

still clueless...i'm just not getting it.

Answer 12

did you get \[\Large \frac{1}{27^{\frac{3}{2}}}\]

Answer 13

no

Answer 14

\[\large x^{-\frac{3}{2}} = 27\] \[\large (x^{-\frac{3}{2}})^{-1} = 27^{-1}\] \[\large x^{\frac{3}{2}} = \frac{1}{27}\] lol sorry i got confused...is that what you got so far?

Answer 15

to solve
\[ x^{-\frac{3}{2}} = 27 \]
use the rule
\[ (x^a)^b= x^{ab} \]
raise both sides to to -2/3 power (this makes the left side just x)

Answer 16

to make sense of
\[ 27^{-2/3} \]
remember: minus means flip : \( 1/27^{2/3} \)
1/3 means take the cube root
2 means square

Answer 17

im'm totally confused now

Answer 18

start with
\[ x^{-\frac{3}{2}}= 27 \]
raise both sides to -2/3
\[ (x^{-\frac{3}{2}})^{-\frac{2}{3}}= 27^{-\frac{2}{3}} \]

Answer 19

can you simplify the left side? You multiply the exponents.
you get
\[ x^1 = 27^{-\frac{2}{3} } \]

Answer 20

ok. so to solve the problem would it be x=1/9

Answer 21

For the right side, we can write it as
\[ (27^{\frac{1}{3}})^{-2} \]
Do you see how?

\[ 27^{\frac{1}{3}} \]
means take the cube root of 27. 27= 3*3*3
can you find the cube root?

Answer 22

3^3

Answer 23

yes 27= 3^3
and
\[ (3^3)^{\frac{1}{3}} \] is ??

Answer 24

we find
\[ 27^{\frac{1}{3}} = 3\]
so now we have
\[ (27^{\frac{1}{3}})^{-2} = 3^{-2} \]

Answer 25

1/cube root of 3

Answer 26

i am so much more confused now

Answer 27

step by step
we have
\[ (27^{\frac{1}{3}})^{-2} = 3^{-2} = ?? \]

Answer 28

1/9

Answer 29

Yes. x= 1/9
If you are confused, go back and try to follow the rules we used to get to the answer.

Answer 30

ok...i will. i have to remember this before my final. thanks so much for the step by step.

Answer 31

The very first step was to know how to change
logx(27)=-3/2

into
\[ x^{-3/2} = 27 \]

Answer 32

btw, it looks like you got the answer at the very beginning.

Answer 33

thax