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#.