Question

Help last question!!

Explain he steps you would use to solve the equation. Find the solution.
8^2x=4096

Answer 1

I have no Idea

Answer 2

Ok, thank you for trying @116601

Answer 3

@mcnabkt

Answer 4

http://www.algebra.com/services/rendering/simplifier.mpl

Answer 5

Write your problem (numbers) and scroll down and it gives you detailed information

Answer 6

@feathert03s

Answer 7

@lizz123 i want the x to be up with the 2 how do i do that

Answer 8

you write the 2 with the x

it does numbers and letters

Answer 9

This is what its doing
i need it to have 2x as an exponent

Answer 10

@lizz123

Answer 11

oh idk sorry

Answer 12

Hint: Express both sides as a power of 8.
\(\Large 8^{2x}=4096=8^4\)
Solve for x.

Answer 13

what? that doesn't make sense

Answer 14

where did you get ^4 from @mathmate

Answer 15

@calculusfunctions

Answer 16

@SolomonZelman

Answer 17

If you keep dividing 4096 by eight, and count how many times you divide before you get a one.
I.e. 4096/8/8.../8 will tell you 8*8*..*8 = 8 raised to how many times will give 4096.

Answer 18

The other way to do it is to factorize 4096 into powers of two, and work from there.

Answer 19

ohk so x=?

Answer 20

Try to equate the bases (which you can in your question). In other words, first write 4096 as a power of 8.

Answer 21

we have 8^4

Answer 22

So that's the right hand side of 8^4.
Can you now solve for x?

Answer 23

no because there are two =

Answer 24

Since the 4th power of 8 is 4096,\[8^{2x}=4096\]is equivalent to\[8^{2x}=8^{4}\]Now if the bases are equal, then the exponents are equal. Thus\[2x =4\]

Answer 25

Understand @feathert03s ?

Answer 26

The middle is just an intermediate step.
The left hand side still equals the right hand side, right?

Answer 27

ok, so i put
8^22 = 4096 = 8^4

8^2x = 8^4

2x= 4

Answer 28

Yes!

Answer 29

Now solve for x.

Answer 30

Absolutely! \(\color{blue}{\Large\checkmark}{Correct!}\)

Answer 31

x=2

Answer 32

You got it!

Answer 33

sweet thank you both!!

Answer 34

You're welcome! :)

Answer 35

Welcome!