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JcAlmighty

The answer is \(x= \frac{log_{10} (243 )}{log_{10} (3 )}\)

\(3^{x} =243\)
Logarithm both sides of the equation:
\(log_{10} (3^{x} ) = log_{10} (243 )\)
Since: \(log (a^{b}) = b*log(a)\), then: \(log_{10} (3^{x} ) =x*log_{10} (3 )\)
Back to our equation:
\(log_{10} (3^{x} ) = log_{10} (243 ) \\ x*log_{10} (3 ) = log_{10} (243 ) \\ x= \frac{log_{10} (243 )}{log_{10} (3 )}\)

The logarithmic form of the equation in base 10 will be log 3ˣ = log 243. Then the value of x is 3.

What is an exponent?

Let a be the base and x is the power of the exponent function and b be the y-intercept. The exponent is given as

y = aˣ + b

Given the exponential equation 3ˣ = 243

Then the logarithmic form of the equation in base 10 will be

Taking log on both sides, then we have

 log 3ˣ = log 243

 log 3ˣ = log 3⁵

x log 3 = 5 log 3

        x = 5

More about the exponent link is given below.

https://brainly.com/question/5497425

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