Question

i need help!!!! solving cube root of 2^3=3/2

Answer 1

first do i get the cube root of 2^3?, idk what to do after that

Answer 2

\[2^3=\frac{3}{2}\] that is false, so something is missing

Answer 3

This isn't an equation. Did you leave out a variable? Without one, this statement is just saying 2 = 1.5.

Answer 4

\[\sqrt[3]{2^3}=2\]

Answer 5

oh, sorry, i'm knew to this. . . cube root of 2^3x = 3/2

Answer 6

is it
\[2^{3x}=\frac{3}{2}\]?

Answer 7

or
\[\sqrt[3]{2^{3x}}=\frac{3}{2}\]?

Answer 8

if second one then
\[\sqrt[3]{2^{3x}}=2^x\]

Answer 9

the second one

Answer 10

so your equation is
\[2^x=\frac{3}{2}\]

Answer 11

to solve this for x you have to use logarithms.

Answer 12

no, the one with the 3 outside of the square root

Answer 13

we start with
\[\sqrt[3]{2^{3x}}\] yes? which means the cube root?

Answer 14

right

Answer 15

ok now this means the cube root of
\[2^3x]

Answer 16

cube root of
\[2^{3x}\]

Answer 17

and the cube root of
\[2^{3x}\] is
\[2^x\]

Answer 18

because the 3's cancel?

Answer 19

in other words
\[\sqrt[3]{2^{3x}}=2^x\]\]

Answer 20

yes you can think of it that way.

Answer 21

ok

Answer 22

the cube root of something cubed is just the somehting

Answer 23

oh, alright

Answer 24

so now we have
\[2^x=\frac{3}{2}\]

Answer 25

and we want x

Answer 26

so we gotta get x to be a base?

Answer 27

but we don't know it because
\[2^1=2, 2^2=4, 2^3=8,...\]

Answer 28

so you have to use logarithms go get it

Answer 29

\[\sqrt[3]{2^{3x}}=2^\frac{3x}{3}=2^x\]
i wrote it like this just to show you another way of writing it

Answer 30

we go right to the answer

Answer 31

so solve
\[A=b^x\] for x we write
\[x=\frac{\ln(A)}{\ln(b)}\] in other words the log of the total divided by the log of the base

Answer 32

\[\log_2(2^x)=\log_2(\frac{3}{2})\]
\[x=\log_2(\frac{3}{2})\]

Answer 33

in this case
\[b=2\]
\[A=\frac{3}{2}\] so our answer is
\[x=\frac{\ln(\frac{3}{2})}{\ln(2)}\]

Answer 34

hello my myininaya!

Answer 35

or using change of base formula you can get what satellite got

Answer 36

hey

Answer 37

well i have to object to what you wrote

Answer 38

no no!

Answer 39

to say that
\[b^x=A\] means
\[x=\log_b(x)\] contains no infromation

Answer 40

i mean it is true, don't get me wrong
but they say the same thing exactly

Answer 41

since
\[lob_b(x)\] means the number you raise b to to get x. so this is a tautology

Answer 42

right you are just writing in in logarithm form

Answer 43

it "solves' nothing. just rewrites it in a different form

Answer 44

like saying solve
\[x^2=2\] and getting
\[x=\pm\sqrt{2}\] a miserable tautology

Answer 45

one means find the number whose square is two. and math teacher answer says ok the number whose square is two. thanks for nothing

Answer 46

\[\log_b(a)=\frac{lna}{lnb}\]
my answer is only one step from your answer using change of base

Answer 47

yes of course. but to me "change of base" means to solve
\[b^x=A\] for x you get \[x=\frac{\ln(A)}{\ln(b)}\]

Answer 48

you are so competitive lol

Answer 49

i want the number you raise b to to get A and that is my answer. now i have some hope of finding it. especially since log is a well defined function

Answer 50

they should have the math Olympics

Answer 51

yes, that is me \[\color{green}{\text{mr competitive}}\]

Answer 52

any way ms graceful, hope you got an answer you like out of this one way or another.
my myininaya is the best for sure!