What is the logarithmic form of the equation e^(3x) = 3247?

To convert the equation e^3x = 3247 into logarithmic form, we start by understanding the relationship between exponential and logarithmic functions.

The general form of an exponential equation is b^y = x, which can be rewritten in logarithmic form as y = log_b(x). In this case, e serves as the base of the exponent.

Following this rule, we can represent the equation e^3x = 3247 in logarithmic form as:

3x = ln(3247)

Where ln denotes the natural logarithm, which is the logarithm to the base e. To isolate x, you would divide both sides by 3:

x = (ln(3247)) / 3

This simplified expression provides the value of x in terms of the natural logarithm of 3247.

In summary, the logarithmic form of the equation e^3x = 3247 is:

3x = ln(3247)

And if needed, you can solve for x as:

x = (ln(3247)) / 3