Respuesta :
- The solution of given logarithmic equation is:
= [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]
Step-by-step explanation:
Given that
- The logarithmic equation
[tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]
To find
- The solution of this given logarithmic equation
So, according to the question
we have,
- The logarithmic equation
[tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]
We know that,
∵ log(m.n) = logm + logn
Now using this property to solve that logarithmic equation
= [tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]
= [tex]logx+log(x^2 + 3 )^{\frac{-1}{2} }[/tex]
We know that,
∵ log(mⁿ) = nlogm
Now using this property to solve that logarithmic equation
= [tex]logx+log(x^2 + 3 )^{\frac{-1}{2} }[/tex]
= [tex]logx+({\frac{-1}{2} )log(x^2 + 3 )[/tex]
= [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]
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:
- = [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]
To learn more about logarithmic equation, please click on the link:
https://brainly.com/question/10025117
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