Question

Fractional indices, please answer the following questions while showing all the steps. thank you.

Find the value of x when:

1) 4^x = 64

2) x^2 = 4/9

3) 8^x = 2

Answer 1

\[4^x=4^3\]

Answer 2

therefore wth same base x ll be 3

Answer 3

\[2)x^2=4/9\]

Answer 4

ll be
multiply by 9 both side

Answer 5

\[9(x^2)=(4/9)9\]

Answer 6

\[9x^2=4\]

Answer 7

\[(3x)^2=2^2\]

Answer 8

therefore same power ll be

Answer 9

\[3x=2\]

Answer 10

Could you please answer #1 again, i did not understand

Answer 11

divide by 3 both side

Answer 12

\[x=2/3\]

Answer 13

but how do you know to divide by 3?

Answer 14

coz we find the value of x if it like this 3x=2 u should divide by 3

Answer 15

let me show you an example of another question. and using that help me answer these questions okay.

Answer 16

okay

Answer 17

here is an example: 16^1/4 = 4sqrrt16 = 2

Answer 18

thats the method we are using

Answer 19

one sec let me show you a drawing

Answer 20

u mean \[16^1/4=4\sqrt{16}=2\]