Question

Show that log1000= 3 log2+3log5

Answer 1

Answer:

The key rule you need to refer to is:

 log ab = log a + log b

So

    log 1000 = log ( 10 × 10 × 10 )

 = log ( 2 × 2 × 2 × 5 × 5 × 5 )

 = log 2 + log 2 + log 2 + log 5 + log 5 + log 5

 = 3 log 2  +  3 log 5

This can be made a bit shorter if you also use the rule:

 log aⁿ = n log a

Then it is just

   log 1000

= log ( 2³ × 5³ )

= log 2³  +  log 5³

= 3 log 2  +  3 log 5

Hope this helps!