How do you evaluate this expression below? `log_6[(1/1296)^3]`

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mathsworkmusic eNotes educator| Certified Educator

Using that log(a^b) = b x log(a)

`log_6[(1/1296)^3] = log_6(1296^(-3)) = -3log_6(1296)`

The logarithm of a number `x` base `r`, `log_r(x)`, is the power to which we need to raise `r` to obtain `x` . So here, we ask what power do we need to raise `r=6` to in order to obtain `x=1296`? We find that 6^4 = 1296, so we need to raise 6 to the power 4 to obtain 1296. Therefore

`-3log_6(1296) = -3 times 4 = -12`


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