Question

I need help with a question

Answer 1

Exponential function

Part A

We know that

`2^6=64`

then

`\begin{gathered} (2^6)^x=1 \\ 64^x=1 \end{gathered}`

then, we want to find a value of x so if we multiply x times 64 it will be 1.

We know that any number with exponent 0 is 1:

`64^0=1`

Then x = 0

Part B

Since any number with exponent 0 is 1, then:

`5^0=1`

Then,

`\begin{gathered} (5^0)^x=1 \\ 1^x=1 \end{gathered}`

So, we want to find a number for x so if 1 is multiplied x times it will be 1.

Everytime 1 is multiplied by itself the answer is 1:

`\begin{gathered} 1^2=1\cdot1=1 \\ 1^4=1\cdot1\cdot1\cdot1=1 \\ 1^(-2)=(1)/(1)\cdot(1)/(1)=1 \end{gathered}`

Then, x is any number

x = ..., -2, -1, 0 , 1, 2, ...