Question

If `x = log  3/7, y = log  10/7, z = log  10/3`, find the value of `5^(x  -  y  +  z)`.

Answer 1

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

Step-wise calculation:

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

= `log [(3/7) ÷ (10/7)] + log (10/3)`

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

= `log [(3/10) xx (10/3)]`

= log (1)

= 0

`5^(x  -  y  +  z)`

= 5⁰

= 1