What is "given the exponential equation 3x = 243?

The exponential equation 3x=243 can be rewritten as 3^x=3^5. This means that the value of x that satisfies the equation is 5, since 3^5=243.

In general, exponential equations of the form a^x=b can be solved by taking the logarithm of both sides. Specifically, if we take the logarithm of base a on both sides of the equation, we get:

x=log_a(b)

This means that x is the logarithm of the value b with respect to the base a.

For example, in the given equation 3x=243, we can rewrite it as:

x = log_3(243)

And we know that log_3(243)=5, so x=5.

Exponential equations and logarithms are important in many areas of mathematics, science, and engineering, and are used to model growth, decay, and other phenomena.