Due tomorrow please help :)

Question

1.) 8 to the power of x equals 1/8

Answer 1

we start with

 

8^x = 1/8 

 

we know 1/8 = 8^-1      1/8 and 8 are reciprocals

 

the equation becomes

 

8^x= 8^-1

 

if two powers with the same base are equal, then the exponents must also be equal

 

Therefore, x = -1

Answer 2

Except for zero, a real number R raised to the (-1) power becomes the fraction 1/R.

 

Your question asks if the real number is 8, what exponent will make it 1/8?

 

Do you see what the exponent will be? If not just comment this and I will give you the answer. I hope this helps.

Answer 3

For this you are trying to find x for:

 

8^x=(1/8)

 

You could remember that a number to the power of -1 equals the reciprocal of that number (making the answer to this problem -1), but I think the point of this is for you to learn about logarithms (maybe).

 

The way I remember to do this is with this:

 

"log with a base of ___ and an answer of ___ has an exponent of ___"

 

Looking at your problem, we have:

 

"log with a base of 8 and an answer of (1/8) has an exponent of x"

 

So what you would input into a calculator is:

 

log ₈ (1/8) =

 

and the answer you would get is -1.

Answer 4

The reciprocal of any non-zero number is that number to the -1 power. For your problem, since 1/8 is the reciprocal of 8,  8^x = 1/8 means that  x= -1.