Final answer:
The exponential statement 4^(2x-1)=1024 can be converted to logarithmic form as log4(1024) = 2x - 1. Since 4^5 = 1024, we confirm that the correct logarithmic form is indeed log4(1024) = 5, which further simplifies to give 2x - 1 = 5.
Step-by-step explanation:
To convert the exponential statement 4^(2x-1)=1024 to logarithmic form, you need to use the definition of a logarithm as the inverse of an exponential function. The general form of a logarithm is logb(a) = c which is equivalent to b^c = a. In this case, we can say the base (b) is 4, the exponent we are looking for (c) is 2x - 1, and the result the base is raised to (a) is 1024.
Using this information, we can write the logarithmic form of the equation as log4(1024) = 2x - 1.
To prove this, we can remember that 4^5 = 1024, so the logarithmic equation simplifies to log4(4^5) = 5 due to the property that if b^c = a, then logb(a) = c. Thus, we can also say that log4(1024) = 5, and this tells us that 2x - 1 = 5.