Question

Log(x(x^2 + 3)^−1/2)

Answer 1

• The solution of given logarithmic equation is:

          =  $logx-{\frac{1}{2} log(x^2 + 3 )$

Step-by-step explanation:

Given that

• The logarithmic equation

            $log(x.(x^2 + 3 )^{\frac{-1}{2} })$

To find

• The solution of this given logarithmic equation

So, according to the question

we have,

• The logarithmic equation

            $log(x.(x^2 + 3 )^{\frac{-1}{2} })$

We know that,

    ∵ log(m.n) = logm + logn

Now using this property to solve that logarithmic equation

          =  $log(x.(x^2 + 3 )^{\frac{-1}{2} })$

          =  $logx+log(x^2 + 3 )^{\frac{-1}{2} }$

We know that,

    ∵ log(mⁿ) = nlogm

Now using this property to solve that logarithmic equation

          =  $logx+log(x^2 + 3 )^{\frac{-1}{2} }$

          =  $logx+({\frac{-1}{2} )log(x^2 + 3 )$

          =  $logx-{\frac{1}{2} log(x^2 + 3 )$

This is the the solution of given logarithmic equation.

Logarithmic equation.

• The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number. The logarithm, in its most basic form, counts the number of times the same factor appears when multiplied repeatedly; for instance, since 1000 = 10 x 10 x 10 = 103, its "logarithm base 10" is 3, or log10 (1000) = 3. When there is no possibility of confusion or when the base is irrelevant, as in big O notation, the logarithm of x to base a is written as logₐ (x), logₐ x, or even without the explicit base, log x.

Answer:

•           =  $logx-{\frac{1}{2} log(x^2 + 3 )$

To learn more about logarithmic equation, please click on the link:

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