Respuesta :
Answer: [tex]log_39=2[/tex] is the logarithmic equation which is equivalent to[tex]3^2=9[/tex].
Step-by-step explanation:
According to the laws of logarithms
[tex]log_b\ x=n[/tex] ,where b=base ,n,x all are positive
It can be written in exponential form such as
[tex]x=b^n[/tex]
Now in the given question x=9 ,b=3 and n=2 such that it will equals to
[tex]log_39=2[/tex]
Hence the logarithmic equation for [tex]3^2=9[/tex] is[tex]log_39=2[/tex].
Logarithmic equation is a equation which contains the logarithmic function of variables or constant.
The equivalent logarithmic equation of the given equation is,
[tex]\log_3( 9)=2[/tex]
The given equation has to be convert in the form of logarithmic equation.
What is logarithmic equation?
Logarithmic equation is a equation which contains the logarithmic function of variables or constant.
Given information-
The equivalent result of logarithmic equation given in the problem is
[tex]3^2=9[/tex]
Taking log (base 3) both side,
[tex]\log_3(3^2)=\log_3( 9)[/tex]
By the power rule, the power of log can be written at the front of the logarithmic function. Thus,
[tex]2\log_3(3)=\log_3( 9)[/tex]
By the identity rule, when the base and argument of log is same, then the result is 1. Thus,
[tex]2\times (1)=\log_3( 9)[/tex]
Rewrite the equation as,
[tex]\log_3( 9)=2[/tex]
Hence the equivalent logarithmic equation of the given equation is,
[tex]\log_3( 9)=2[/tex]
Learn more about the logarithmic equation here;
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