What is #log_(1/2) 4#?

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Answer 1 · 2016-09-29T03:36:07

#-2#

You can rewrite this question easily as

#(1/2)^x=4#

That is the purpose of a log: to find the value of the exponent. For this problem, we simply rewrite it and the do some math. Since

#1/2 < 1" "# and #" "4 > 1#

we know the exponent must be negative. That allows us to write the equation as

#2^(-x) = 4#

So, #2# to the power of what gets us #4#? The answer is #2#

#2^2=4#

Thus, you get #-2#.