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

1 Answer
Aug 30, 2016

Answer:

#x = 2.916#

Explanation:

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.