Question

how can i solve 4^{3x=1}=16,384?

Answer 1

using properties of logs and or exponents

Answer 2

exponent

Answer 3

\[\Large B^{m+n}=B^m*B^n\]

Answer 4

divide of the 4^(=1?) part and try to get the right side into a base 4 equivalent

Answer 5

another thought is that since 4 = 2^2 we can try to turn it all into base 2 stuff

Answer 6

\[4^{3x+1}=16,384\]

Answer 7

use the property i started with\[4^{3x+1}=4^{3x}*4^1\]

Answer 8

divide off the 4^1 from each side to lessen that number

Answer 9

4021
----------
4 ) 16384

Answer 10

ok

Answer 11

\[4^{3x}=4021\]
is what we have left to figure on

Answer 12

ok

Answer 13

if you are just forced to deal with exponents; lets write up a base 4 table

^5 ^4 ^3 ^2 ^1 ^0
1024 256 64 16 4 1

Answer 14

4^6 = 4096

Answer 15

i see

Answer 16

and it helps if i learn to divide; 16384/4 = 4096 too

Answer 17

so, that leaves us with\[4^{3x}=4^6\]

equate exponents

3x=6 when x=?

Answer 18

so x= 6?

Answer 19

3x = 6

Answer 20

ok thx