This theorem says that, if we take the log of an exponential, and the bases are the same, then the output is the exponent.

For example:

log₂(2³) = 3

We can confirm this by evaluating the logarithm on the left. We know that:

2³ = 8

Using substitution:

log₂(2³) = log₂8

We also know that:

log₂8 = 3

Thus:

log₂(2³) = 3

Quiz (1 point)

• if x^p = z, then log_x(x^p) = log_xz

• if x^p = z, then log_xz = p

• if the following are true:

  • a = b
  • b = c

  then a = c

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.

Step	Claim	Reason (optional)	Error Message (if any)
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