Given the exponential equation 3^x = 27, what is the logarithmic form of the equation in base 10?

The exponential equation 3^x = 27 can be converted into logarithmic form. To do this, we need to recognize that the logarithm is the inverse operation of exponentiation.

First, we can express 27 as a power of 3: 27 = 3³. Therefore, we can rewrite the original equation as:

3^x = 3³

Now, since the bases are the same, we can set the exponents equal to each other:

x = 3

To express this in logarithmic form, we write:

x = log₃(27)

This means that the logarithm of 27 to the base 3 is equal to x. However, since you asked for the logarithmic form in base 10, we can use the change of base formula:

log₃(27) = log₁₀(27) / log₁₀(3)

So, in the final answer, while x = 3 or the primary logarithmic form would be:

x = log₃(27)

To convert it into a base 10 logarithmic expression:

x = log₁₀(27) / log₁₀(3)

This gives you the logarithmic form of the equation in terms of base 10.