Question

4^3x=512, then x= ??

Answer 1

x would equal 1.5. 1.5 times 3 would eual 4.5. 4^4.5 equals 512.

Answer 2

can ya do it step by step ?

Answer 3

a^(b*c)=(a^b)^c=so 4^(3x)=(4^3)^x=64^x so x=log(64)512

Answer 4

still dont get it ......... :/

Answer 5

I kinda did guess and check. 4^3*5 would equal 1024 so that would be too high so if you try 4 is would equal 256 which is to low. You kind of just have to find something in between. So if you tried 4^3*4.5 it would be 512 :D

Answer 6

Well 4^3x=(4^3)^x=64^x
I hope you get it so far.
Now 512/64= 8 So 64*8=512 so 64*sqrt(64)=512 so (64^1)*(64^(1/2))=512 so 64^1,5=512 so x=1,5
Tell me what you dont get i will try to make it clear

Answer 7

cant get this "so 64^1,5=512 so x=1,5"

Answer 8

Well if you know that 4^3x=64^x and 64^x=512 and 64^1,5=512 so 64^x=64^1,5 so x=1,5

Answer 9

i got ur method @alejandros but i cant use the calculator (not allowed)..........

Answer 10

its easy with the calculator ................i need to know a way through which i can get my answer without calculator ..

Answer 11

I just to ld you XD. You do undestand that 4^3x=64^x ?

Answer 12

yup i do it like (4*4*4) right ?? and then x is left

Answer 13

Yeah so now we know that 64^x=512. So we divide both sides by 64.
Now we have 64^(x-1)=512/64=8 Tellme where do you stop understanding ;]
Now we know that 64^(x-1)=8 However 8 is square root of 64 and we can write square root of something as a power of 1/2, as long as it is positive and 64>0.
\[\sqrt{a}=a^{1/2}\]
So know we know that 64^(x-1)=64^(0,5) So x-1=0,5 so x=1,5

Answer 14

64^(x-1) where did x-1 came from '.' ???

Answer 15

\[a^x/a^z=a^(x-z) \]
And 64=64^1

Answer 16

oh ok ty very much :)