To convert the exponential equation 4x = 64 into its logarithmic form in base 10, we need to follow a specific relationship between exponential and logarithmic expressions. The general principle is that if you have an equation in the form by = z, it can be expressed in logarithmic form as y = logb(z).
In our case, we have:
- b is 4
- y is x
- z is 64
Thus, we can express the given equation in logarithmic form as:
x = log4(64)
Next, since the question asks for the logarithmic form in base 10, we can convert log base 4 to log base 10 using the change of base formula:
log4(64) = log10(64) / log10(4)
Therefore, in base 10, the logarithmic form of the original equation 4x = 64 can be expressed as:
x = log10(64) / log10(4)
This completes the transformation from the exponential form to the logarithmic form in base 10.