Question

If x = (100)^a , y = (10000)^b and z = (10)^c , find log`(10sqrty)/( x^2z^3)` in terms of a, b and c.

Answer 1

x = (100)^a , y = (10000)^b and z = (10)^c

⇒ log x = alog 100, log y = b log 10000 and log z = clog 10

`"log"(10sqrty)/(x^2z^3)` = log10√y - log( x²z³ )

= log( 10y^1/2 ) - logx² - logz³

= log 10 + logy^1/2 - logx² - logz³
= log 10  + `1/2`log y - 2log x - 3log z

= 1 + `1/2log(10000)^b - 2log(100)^a - 3log(10)^c`       ....(Since log 10 = 1 )

= 1 + `b/2log(10)^4 - alog(10)^2 - 3clog10`

= 1 + `b/2 xx 4log10 - 2 xx 2alog 10 - 3clog10`

= 1 + 2b - 4a - 3c