how do i write 32 using an exponent and a base of 2?

32=4x8

= 2^2 x 2^3
=2^5

To write 32 using an exponent and a base of 2, you need to determine the value of the exponent that, when raised to 2, will result in 32.

Here's how you can do it step by step:

1. Start by considering the base, which is 2 in this case.
2. Determine the exponent by asking yourself, "To what power should I raise the base 2 to get 32?"
3. Now, you need to find a number, "x," that satisfies the equation 2^x = 32.
4. To find the value of "x," you can take the logarithm of both sides of the equation.
- You can use the common logarithm (log base 10) or the natural logarithm (log base e or ln) in this step. Let's use the natural logarithm (ln) here.
- Take the ln of both sides: ln(2^x) = ln(32).
- Using the logarithmic property, you can bring down the exponent in front: x * ln(2) = ln(32).
5. Now, divide both sides of the equation by ln(2) to solve for x: x = ln(32) / ln(2).

Calculating this using a calculator, you'll find that x ≈ 5. By substituting this value back into the original equation 2^x = 32, you can verify the answer: 2^5 = 32.

So, by using an exponent and a base of 2, you can write 32 as 2^5.