Question

2^x = 64

Answer 1

\[1/2^-x = 64/1\]

Answer 2

ok, so for questions like this, it often helps if you can reduce the equation down to something like:\[a^x=a^y\]because then you can immediately deduce that x=y

Answer 3

so here you are given:\[2^x=64\]so you need to see if you can express 64 as a power of 2

Answer 4

as a power of 2?

Answer 5

How do you know that

Answer 6

yes, because you have a power of 2 on the left-hand-side

Answer 7

isnt the power x because the equation is 2^x

Answer 8

it is 2 to the power of x

Answer 9

so it is a "power of 2" expression

Answer 10

arright

Answer 11

so, for 64, start with 2 and keep multiplying by 2 until you get to 64

Answer 12

with practice you will learn to recognise some well known powers of 2

Answer 13

8?2 is 64 but how do I show that while soilveing it

Answer 14

8^2*

Answer 15

start with 2, so:\[2^1=2\\
2^2=2*2^1=4\\
2^3=2*2^2=8\]etc

Answer 16

Our teacher looks for proper form while solving, so how do I show my work while solving the equation, just by looking at it i can easily tell it was 8 but I dont understand how to properly show my work to find x

Answer 17

I understand - all you need to show is how you got 64 by multiplying 2's together - as I started showing you above. then you can proceed to solve the question given to you.

and remember, we are looking for a power of 2 and not a power of 8

Answer 18

you could work backwards as well by taking square roots at each step as follows:
\[2^x =64\]\[=(8)^2\]\[=((4)^2)^2\]etc

Answer 19

until you get to 2 inside the brackets

Answer 20

e.g. suppose you had to solve:\[3^x=27\]we could do it like this:\[3^x=81\]\[=(9)^2\]\[=((3)^2)^2\]\[=3^4\]therefore:\[x=4\]

Answer 21

*I meant 81 on the first line up there

Answer 22

not 27

Answer 23

that is an example of the "backwards" solution I was talking about

Answer 24

alternatively, you could solve it as follows:\[3^1=3\]\[3^2=3*3^1=9\]\[3^3=3*3^2=27\]\[3^4=3*3^3=81\]therefore:\[81=3^4\]therefore, if:\[3^x=81\]then:\[3^x=3^4\]therefore:\[x=4\]

Answer 25

x = 6 for this problem

Answer 26

correct :)