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PLEASE HELP I HAVE 30 POINTS Part A: If (6^2)^x = 1, what is the value of x? Explain your answer. (5 points) Part B: If (6^0)^x = 1, what are the possible values of x? Explain your answer. (5 points)

User Luzo
by
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1 Answer

4 votes

Answer:

Part A: 0

Part B: All real numbers

Explanation:

Part A:

We have:


(6^2)^x=1

First, let's evaluate the square:


36^x=1

Now, what to the xth power will equal 1?

Remember the fact that anything (except for 0) to the zeroth power is 1.

Therefore, our x is 0:


36^0=1

Part B:

We have:


(6^0)^x=1

Like mentioned previously, anything to the zeroth power is 1. Thus:


1^x=1

Now, 1 is a special base because 1 to any (real) power is still going to be 1. For example:


1^0=1,1^1=1,1^(999),\text{ and } 1^(\pi)=1

Therefore, our values of x is all real numbers.

And we're done!

User Dyngberg
by
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