What is the solution to the logarithmic equation log4(x) = 1032/5?

To solve the equation log4(x) = 1032/5, we need to rewrite it in exponential form. The equation states that x is equal to 4 raised to the power of 1032/5:

So, we express this as:

x = 41032/5

Next, we can simplify the base further. Since 4 can be expressed as 22, we rewrite x as:

x = (22)1032/5

Using the power of a power property of exponents, we can multiply the exponents:

x = 2(2 * 1032/5)

This simplifies to:

x = 2(2064/5)

Finally, dividing 2064 by 5 gives us:

x = 2412.8

Thus, the solution to the equation log4(x) = 1032/5 is:

x = 2412.8

This means that the value of x can be expressed as a power of 2, which is approximately x ≈ 4.7187 × 10124 when evaluated.