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Chapter 12: Problem 3

Write each equation in its equivalent exponential form. $$2=\log _{3} x$$

Short Answer

Expert verified
The exponential form of the given logarithmic equation \(2 = log_3 x\) is \(3^2 = x\), which simplifies to \(x = 9\).

Step by step solution

01

Analysis of the given equation

You have been given a logarithmic equation \(2 = log_3 x\). This equation involves a base of 3, a logarithm of 2, and an argument of x.
02

Transformation into exponential form

Remembering the definition of logarithm, transform the equation from logarithmic form to exponential form using the principle \(a^b = x\), where a is the base of the logarithm, b is the value of the logarithm, and x is the number being taken the logarithm of. Apply this principle to the given equation and translate it to exponential form which will result in \(3^2 = x\).

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