Given the exponential equation 4^x = 64, what is the logarithmic form of the equation in base 10?
x = log base 2 of 64, all over log base 2 of 4
x = log base 2 of 4, all over log base 2 of 64
x = log base 10 of 64, all over log base 10 of 4
x = log base 10 of 4, all over log base 10 of 64

Solution:

Given: Exponential equation 4^x = 64

We need to convert the above equation in logarithmic form,

First apply log both sides with base 10

log₁₀4^x = log₁₀64

We know that,

log a^m = m loga

x log₁₀4 = log₁₀64

Now, divide by log₁₀4 both sides

x = log₁₀64 / log₁₀4

Therefore, the logarithmic form of the equation in base 10 is x = log₁₀64 / log₁₀4.

Given the exponential equation 4^x = 64, what is the logarithmic form of the equation in base 10?

Summary:

Given the exponential equation 4^x = 64, the logarithmic form of the equation in base 10 is x = log₁₀64 / log₁₀4.