Question

Given x = log₁₀12 , y = log₄ 2 x log₁₀9 and z = log₁₀0.4 , find :
(i) x - y - z
(ii) 13^{x - y - z}

Answer 1

(i) x - y - z

= log₁₀12 - log₄2 x log₁₀9 - log₁₀0.4

= log₁₀( 4 x 3 ) - log₄2 x log₁₀9 - log₁₀0.4

= log₁₀4 + log₁₀3 - log₄2 x 2log₁₀3 - log₁₀`( 4/10 )`

= log₁₀4 + log₁₀3 - `(log_10 2)/(2log_10 2)` x 2log₁₀3 - log₁₀4 + log₁₀10
= log₁₀4 + log₁₀3 - `[ 2log_10 3 ]/2`- log₁₀4 + 1
= 1

(ii) 13^{x - y - z} = 13¹ = 13.