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JeanaShupp

Answer:  \(log_39=2\) is the logarithmic equation which is equivalent to\(3^2=9\).


Step-by-step explanation:

According to the laws of logarithms

\(log_b\ x=n\) ,where b=base ,n,x all are positive

It can be written in exponential form such as

\(x=b^n\)

Now in the given question x=9 ,b=3 and n=2 such that it will equals to

\(log_39=2\)

Hence the logarithmic equation for \(3^2=9\) is\(log_39=2\).

Logarithmic equation is a equation which contains the logarithmic function of variables or constant.

The equivalent logarithmic equation of the  given equation is,

\(\log_3( 9)=2\)

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

\(3^2=9\)

Taking log (base 3) both side,

\(\log_3(3^2)=\log_3( 9)\)

By the power rule, the power of log can be written at the front of the logarithmic function. Thus,

\(2\log_3(3)=\log_3( 9)\)

By the identity rule, when the base and argument of log is same, then the result is 1. Thus,

\(2\times (1)=\log_3( 9)\)

Rewrite the equation as,

\(\log_3( 9)=2\)

Hence the equivalent logarithmic equation of the  given equation is,

\(\log_3( 9)=2\)

Learn more about the logarithmic equation here;

https://brainly.com/question/237321

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