Write each of the following as single logarithm:
` (a) 1+ log_(2) 5" "(b) 2- log_(3) 7`
`(c) 2log_(10) x+3 log_(10) y - 5 log_(10) z`

Answer

(a)`log_(2) 10" "(b) log_(3) 9/7" "(c) log_(10)(x^(2)y^(3))/z^(5)`

Explanation

(a) `1+ log_(2) 5= log_(2) 2+ log_(2) 5 = log_(2) (2 xx5) = log_(2) 10`
(b) `2-log_(3) 7 = 2 log_(3) 3 - log_(3) 7`
`= log_(3) 3 ^(2) - log _(3) 7`
` = log_(3) 9 - log _(3) 7 `
` = log_(3) 9/7`
(c) ` 2log_(10) x+ 3 log_(10) y - 5log_(10) z`
` = log_(10) x^(2) + log _(10) y^(3) - log _(10) z^(5) `
` = log_(10)(x^(2)y^(3)) - log_(10) z^(5) `
` = log_(10). (x^(2)y^3)/z^(5)`