The value of ㏒₁₀√3 - 1 / 2 ㏒₁₀2 is 1 / 2.㏒₁₀(1.5)
Given: To evaluate ㏒₁₀√3 - 1 / 2 . ㏒₁₀2
What are logarithms?
If a equation is given in the form of aᵇ = c, then ㏒ₐc = b or in a definitive way a logarithm is the power to which a number must be raised in order to get a number. As here 'a' is raised to the power 'b' to given a number c, so the number base 'a' if be raised to some power of 'b' then it will yield a number 'c'.
For example, 10² = 100 which can be written as ㏒₁₀100 = 2 by the following property of logarithm that is ㏒ₐ(bⁿ) = n.㏒ₐb.
So, ㏒₁₀100 = ㏒₁₀10² = 2.㏒₁₀10 = 2 [ Another property ㏒ₐa = 1]
Some basic properties on logarithm operations are
1) ㏒ₙa + ㏒ₙb = ㏒ₙ(ab)
2) ㏒ₙa - ㏒ₙb = ㏒ₙ(a / b) [NOTE: ㏒ₙa - ㏒ₙb is not commutative]
3) ㏒ₐ(bⁿ) = n.㏒ₐb
4) ㏒ₐa = 1
Now let's solve the sum: ㏒₁₀√3 - 1 / 2 ㏒₁₀2
㏒₁₀√3 - 1 / 2 ㏒₁₀2 = ㏒₁₀(3)[tex]^{\frac{1}{2}}[/tex] - 1 /2 .㏒₁₀2 [ Root means 1 / 2 power]
= 1 / 2.㏒₁₀(3) - 1 / 2.㏒₁₀(2) [ ㏒ₐ(bⁿ) = n.㏒ₐb ]
= 1 / 2.(㏒₁₀(3) - ㏒₁₀(2))
= 1 / 2.(㏒₁₀(3 / 2) [ ㏒ₙa - ㏒ₙb = ㏒ₙ(a / b) ]
= 1 / 2.㏒₁₀(1.5)
Hence value of ㏒₁₀√3 - 1 / 2 ㏒₁₀2 = 1 / 2.㏒₁₀(1.5)
Know more about "logarithm functions" here: https://brainly.com/question/20785664
#SPJ9
