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 $6^x = 6^(1/3)$

$x = 1/3$

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