Question

What is the value of log 256/ log 1024

Answer 1

Answer:

  0.8

Step-by-step explanation:

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

  $\log_b(a)=\dfrac{\log(a)}{\log(b)}$

__

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

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