Question

please help: 4^x+4 = √2^5x find the value of x.

Answer 1

If you can make the bases equal, you can set the exponents equal to each other.

Answer 2

hmm.

Answer 3

how do i remove the sqared root

Answer 4

You substitute.

Answer 5

I think it is easier to rewrite 4 in terms of sqrt(2) personally.

Answer 6

oh i was thinking like this √2^5x >> 2^5x/2

Answer 7

That works too.

Answer 8

is this right 4^x+4 >> √2^x+6 ?

Answer 9

No.

Answer 10

You already got 2 as a base from the sqrt(2) side. Why not just make a base of 2 on the 4 side too?

Answer 11

4 = 2^2

Answer 12

oh i see 4 sqrt(2) would be 2√2

Answer 13

so 4^x+4 >> √2^x=4 ??

Answer 14

2√2^x+4

Answer 15

I don't understand how or why you did that...

Answer 16

im lost would you show
me how to convert 4 to sqrt(2) please

Answer 17

You said sqrt(2)^5x ->> 2^5x/2
That was a good first step.

Answer 18

You can also rewrite 4^x+4 as 2^2(x+4)

Answer 19

ok so it would be like this 4^x+4 = 2 5x/2
then 2.2^x+4 = 2 ^5x/2
then i operate the exponents
x+4=5x/2

Answer 20

so how do i find x in there

Answer 21

The exponents are 2(x+4) and 5x/2

Answer 22

When you raise an exponent to another exponent, you multiply.

Answer 23

oh yeah i made a mistake 4^x+4 would be 2^2x+4

Answer 24

so it would be like this then 2x+8=2^5x/2 how do i find x in there?

Answer 25

i mean 2x+8=5x/2

Answer 26

Right.

Answer 27

so now 5x=2x+8*2

Answer 28

Right, but distributed.

Answer 29

Don't forget parentheses.

Answer 30

like this 5x=2x+16
5x-2x=16
3x=16
x=16/3

Answer 31

Distribute! 5x=4x+16

Answer 32

The 2 is multiplied by both terms.

Answer 33

oh i seeee

Answer 34

:)

Answer 35

so x would be 16 :|

Answer 36

Right! :)

Answer 37

omg thanks.

Answer 38

i have a 16 question test :}

Answer 39

online

Answer 40

No worries. Just remember to distribute!

Answer 41

hehe.

Answer 42

Test?

Answer 43

yeah

Answer 44

on thatquiz.org

Answer 45

16 question 120 min to answer im so scared

Answer 46

We aren 't allowed to help on tests or quizzes.

Answer 47

oh that too bad/

Answer 48

Or are you prepping for it?

Answer 49

yeah i was

Answer 50

That's cool. Just not during the test itself. :)

Answer 51

Happy studies!do you have some practice problems where you can check your answers?

Answer 52

no really

Answer 53

Those are the best to practice with.

Answer 54

jsut the question for instance this one says calculate log20 + log 5 but i dont have answer anywhere

Answer 55

Is this alg. 2?

Answer 56

you mean algebra 2?

Answer 57

Yeah

Answer 58

yeah that's algebra

Answer 59

i have a test on algebra and geometry

Answer 60

There is a website called Kuta Software that has practice problems with answers for algebra and geometry.

Answer 61

oh thats cool.

Answer 62

is that a software?

Answer 63

Practicing but not knowing if your answers are right or wrong doesn 't help too much in my opinion.

Answer 64

yeah i agree.

Answer 65

You can just download individual pdfs.

Answer 66

Take a look. :)

Answer 67

oh nice

Answer 68

And, by the way, you are in the physics section. This question belongs more in the math one.

Answer 69

yeah i realized that my mistake :| thanks for the website i found the pdfs:)

Answer 70

No worries. Happy studies! :)

Answer 71

JoannaBlackwelder you are awesome. I wish I knew how to give medals or kudos. I just followed this problem out of curiosity but found it very enlightening!

Answer 72

Thanks, @patrickdixon ! You can give me some kudos by clicking the Best response button. Glad it helped you! :)