Question

What is the value of log 256/ log 1024

Answer 1

0.8

Explanation:

The change of base formula for logarithms can be used to find this value exactly. (Your calculator can also tell you.)

`\log_b(a)=(\log(a))/(\log(b))`

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Using this relation with the given numbers, we have ...

`(\log(256))/(\log(1024))=(\log(2^8))/(\log(2^(10)))=(8\cdot\log(2))/(10\cdot\log(2))=(8)/(10)\\\\\boxed{(\log(256))/(\log(1024))=0.8}`