Question

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

Answer 1

Recall that

$\log \frac{a}{b}=\log a-\log b$

Thus, we have

$\log \frac{10z}{4}=\log 10z-\log 4$

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,

$log\frac{10z}{4}=\log 10+\log z-\log 4$