# How do you simplify this expression? 3^log3^7

Luca B. | Certified Educator

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Supposing that you need to simplify the expression `3^(log (3^7))` You need to use the following identity, such that:

`log a^b = b log a`

Hence, reasoning by analogy, yields:

`log (3^7) = 7 log 3`

Hence, substituting `7 log 3`  for `log (3^7)`  yields:

`3^(log (3^7)) = 3^(7 log 3)`

Using the following identity yields:

`(a^b)^c = a^(b*c)`

Reasoning by analogy yields:

`3^(7 log 3) = (3^7)^log 3`

Hence, evaluating the simplified form of the given expression yields `3^(log (3^7)) = (3^7)^log 3.`

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