Final answer:
The logarithmic form of 4⁵ = 1024 is log4(1024) = 5, which shows the power 5 that the base 4 must be raised to in order to get 1024.
Step-by-step explanation:
The logarithmic form of 4⁵ = 1024 is log4(1024) = 5. This means that the number 4 must be raised to the power of 5 to equal 1024. In logarithmic form, the base of the log (in this case, 4) is the same as the base of the exponent in the original expression.
In general, converting an expression from exponential form to logarithmic form involves taking the base of the exponent, which becomes the base of the log, the exponent itself, which becomes the other side of the equation, and the result of the exponentiation, which goes inside the log function. For example, the statement 10³ = 1000 can be expressed in logarithmic form as log10(1000) = 3, because 10 raised to the power of 3 gives us 1000.