Question

if, x = log ₁₀ 12,
y = log₄ 2 * log₁₀ 9 and
z = log₁₀(0.4)
Then find: x-y-z

Answer 1

It is stated that,

x = log ₁₀ 12,

y = log₄ 2 * log₁₀ 9 and

z = log₁₀(0.4)

∴ x-y-z

= log ₁₀ 12 - log₄ 2 * log₁₀ 9 - log₁₀(0.4)

= log ₁₀ 12 - (log₄ √4 * log₁₀ 9) - log₁₀(0.4)

= log ₁₀ 12 - 1/2(log₄ 4 * log₁₀ 9) - log₁₀(0.4)

= log ₁₀ 12 - 1/2 log₁₀ 9 - log₁₀(0.4)

= log ₁₀ 12 - log₁₀ √9 - log₁₀(0.4)

= log ₁₀ 12 - log₁₀ 3 - log₁₀(0.4)

[∵ We know that, in logarithms, (-) is displaced by division]

= log ₁₀ (12/3)  - log₁₀(0.4)

= log ₁₀ 4  - log₁₀(0.4)

[∵ We know that, in logarithms, (-) is displaced by division]

= log ₁₀ (4/0.4)

=log ₁₀ (4*10/4)

= log ₁₀ 10

= 1

So, x-y-z = 1.