How do you find the exact value of #log_6 root3 6#?

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Answer 1 · 2016-12-26T14:49:37

#log_6 6^(1/3) = 1/3#

Let's use laws of indices first.

Another way of writing #" "root3 6" "# is #" "6^(1/3)" "#

The definition of a log is:

The log of a number is the index to which the base must be raised to equal the number.
Apply this definition here: #log_6 6^(1/3)#

#:.log_6 6^(1/3) = 1/3#

Or, using index from: Log form and index form are interchangeable.

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

If #log_6 6^(1/3) = x#, then #6^x = 6^(1/3)#

#x = 1/3#