Question

Part A: If (2^6)^x = 1, what is the value of x? Explain your answer.

Part B: If (5^0)6x = 1, what are the possible values of x? Explain your answer.

Answer 1

HI!!

Answer 2

anything to the power of zero is one

Answer 3

Note that "x" in Part A is an exponent.
Altho' it's not strictly necessary, you might note that 2^6 is "2 to the sixth power."

Answer 4

@3mar

Answer 5

Well, I am here.

Answer 6

question at top

Answer 7

I saw it

Answer 8

For part one: it is an equation that x is in the power not in the base, so it is an exponent equation.

Answer 9

To solve such ones, you would better make all bases the same, then compare the indexes.

Answer 10

In our case:
\[(2^6)^x=1\]
that means that:
\[2^{6x}=1\]
and you may know that any base (number) raised to the power zero equals 1
so we can use that fact to do the following
\[1=2^0\]

Answer 11

An alternative approach would be to apply the natural log operator to both sides of the first given equation. Don't know whether or not you've reached this point yet, but finding a "log" is the "inverse operation" of "exponentiation."

Hope this is a review for you:\[\log 10^x = x\]

\[10^{\log x}=x\]

Answer 12

So we can conclude that:
\[2^{6x}=2^0\]
the same bases >> equal indexes
\[6x=0>>>x=0\]

Got the first part?

Answer 13

yes

Answer 14

Your result?

Answer 15

Can you show me your work for the second?

Answer 16

As 3mar has pointed out, (anything)^0 = 1.

Answer 17

Thank you for the medal!
but let's hit the target firstly.

Answer 18

ok

Answer 19

Can you share yours?

Answer 20

it could be x=1

Answer 21

or x=0

Answer 22

this is for part b

Answer 23

But where your step to determine whichever 1 or 0?

Answer 24

How do you get 0 or 1?

Answer 25

@yolo729
Can you proceed?