How do you evaluate log_64 8?

2 Answers
Ratnaker Mehta
Sep 18, 2016

log_64 8=1/2.

Explanation:

We will use the Defn. of log fun. to find the desired value.

Recall that, log_ba=x iff b^x=a.

So, log_64 8=x rArr 64^x=8 rArr (8^2)^x=8 rArr 8^(2x)=8^1.

As log fun. is 1-1, we must have, 2x=1," giving, "x=1/2.

:. log_64 8=1/2.

anor277
Sep 18, 2016

log_(64)8=1/2

Explanation:

When I write log_ab=c, I ask to what power I raise the base a to get b; the answer here is c, i.e. a^c=b. For log_(10)10, log_(10)100, log_(10)1000, log_(10)1000000, I can immediately write 1,2,3,6 without thinking too much.

For your problem, log_(64)8, I look for the power to which I raise 64 to get 8. But of course, 8^2=64, or sqrt64=8, 64^(1/2)=8. So log_(64)8=1/2.

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