Question

If `x = log  3/7, y = log  10/7, z = log  10/3`, find the value of x – y + z.

Answer 1

Given: `x = log (3/7), y = log (10/7), z = log (10/3)`

Step-wise calculation:

1. `x - y + z = log (3/7) - log (10/7) + log (10/3)`

2. Use log subtraction:

`log (3/7) - log (10/7)`

= `log ((3/7)/(10/7))` 

= `log (3/10)`

3. Then add z:

`log (3/10) + log (10/3)`

= `log (3/10) xx (10/3)` 

= log (1)

4. log (1) = 0