LogEvaluate log _(2) {(1)/(128) }

Question

Log
`Evaluate log _(2) {(1)/(128) }`

Answer 1

128*2+ 1/ 127 =2.00781

Answer 2

9514 1404 393

Answer:

-7

Explanation:

It is helpful to recognize 128 = 2^7. Then you know ...

`\log_2(1)/(128)=\log_2{2^(-7)} =\boxed{-7}`

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If you don't know that, you can use the change of base formula:

`\log_2{(1)/(128)}=\frac{\log{(1)/(128)}}{\log{2}}=(-2.1072)/(0.30103)=\boxed{-7}`