This theorem says that, if we have an exponential operation, and the exponent is a logarithm, and the bases are the same, then the output is the log input.

For example:

2^(log₂8) = 8

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

log₂8 = 3

Using substitution:

2^(log₂8) = 2³

We also know that:

2³ = 8

Thus:

2^(log₂8) = 8

Quiz (1 point)

• if x^p = z, then log_xz = p

• if log_bx = p, then b^(log_bx) = b^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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