How do you calculate #log_4 57# with a calculator?

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Answer 1 · 2016-08-30T21:41:46

#x = 2.916#

Log form and index form are interchangeable.

#log_a b = c hArr a^c = b#

#log_4 57 = x hArr 4^x = 57 larr # (x is between 2 and 3)

The variable is in the index - use logs:

#xlog4 = log57#

#x = log57/log4#

#x = 2.916 larr # (as we expected)

The same result would have been obtained from the change of base law.