Question

Write the following as the sum and/ or differences of logarithm. Assume all variables are positive.

Answer 1

Recall that

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

Thus, we have

`\log (10z)/(4)=\log 10z-\log 4`

Since

`\log ab=\log a+\log b`

we can rewrite the first term, log 10z, as follows

`\log 10z-\log 4=\log 10+\log z-\log 4`

Therefore,

`log(10z)/(4)=\log 10+\log z-\log 4`