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

Solution:

Given: Exponential equation 3^x = 27

We need to convert the above equation in logarithmic form,

First apply log both sides with base 10

log₁₀3^x = log₁₀27

We know, log a^m = m loga

x log₁₀3 = log₁₀27

Now, divide by log₁₀3 both sides

x = log₁₀27 / log₁₀3

Therefore, the logarithmic form of the equation in base 10 is x = log₁₀27 / log₁₀3.

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

Summary:

Given the exponential equation 3^x = 27, the logarithmic form of the exponential equation in base 10 is x = log₁₀27 / log₁₀3.