Question

If x = log 0.6; y = log 1.25 and z = log 3 - 2 log 2, find the values of :
(i) x+y- z       
(ii) 5^{x + y - z}

Answer 1

Given that
x = log 0.6 , y = log 1.25, z = log 3 - 2log 2
Consider
z = log 3 - 2log 2
= log 3 - log 2²
= log 3 - log 4
= log`3/4`
= log 0.75               ....(1)

(i) x + y - z = log 0.6 + log 1.25 - log 0.75

= log`[ 0.6 xx 1.25 ]/0.75`

= log`[0.75/0.75]`

= log 1 
= 0                          ...(2)

(ii) 5^{x + y - z} = 5⁰    ...[ ∵ x + y - z = 0 from (2) ]
= 1