How do you evaluate $log_6 (1/216)$ ?

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Answer 1 · 2016-09-21T17:26:46

$log_6 (1/216) =-3$

Think of a log term asking a question.

$log_10 100$ can be read as..

"What index of 10 gives 100?"
"To what power must 10 be raised to equal 100?"

The answer is 2 because $10^2 = 100$

$log_10 100 = 2$

It really is an advantage to know all the powers up to 1000.

Note that $6^3 = 216$

Write the expression slightly differently as

$log_6 (1/216) = log_6 (1/6^3) = log_6 6^-3$

The answer is now obvious..

"What index of 6 will give $6^-3$ "?

"To what power must 6 be raised to equal $6^-3$ "?

$log_6 (1/216) =-3$

Answer 2 · 2016-09-21T17:33:16

$log_6 (1/216)=-3$ .

If $log_6 (1/216)=x, "then, "6^x=1/216=1/6^3=6^-3......["by, Defn."]$

$rArr x=-3$ .

$:. log_6 (1/216)=-3$ .

How do you evaluate log_6 (1/216)log_6 (1/216)?