Value of 16^log4 5:

To find the value of 16^log4 5, we need to understand logarithms and exponentiation. Let's break down the calculation step by step.

Step 1: Understanding Logarithms
A logarithm is the exponent to which a specified base must be raised to obtain a given value. In this case, the base is 4, and the value is 5. The logarithm of 5 to the base 4 can be written as log4 5.

Step 2: Evaluating Logarithm
To calculate log4 5, we need to find the exponent to which 4 should be raised to get 5. In other words, what power of 4 equals 5? We can write this as:

log4 5 = x, where 4^x = 5

To solve for x, we can take the logarithm of both sides using a common base, such as 10 or the natural logarithm (ln). Let's use the natural logarithm (ln) for this example.

ln(4^x) = ln 5

Using the logarithmic property, we can bring down the exponent:

x * ln 4 = ln 5

Now, divide both sides by ln 4 to solve for x:

x = ln 5 / ln 4

Using a calculator, we can evaluate this expression to find the value of x.

Step 3: Exponentiation
Now that we have found the value of x, we can substitute it back into the original equation:

16^log4 5 = 16^x

Using the value of x, we can calculate the final result using exponentiation.

Step 4: Evaluating the Final Result
Using a calculator or mathematical software, we can compute the value of 16^log4 5 by substituting the value of x into the equation:

16^log4 5 = 16^(ln 5 / ln 4)

Calculating this expression will give us the final result.

Summary:
To find the value of 16^log4 5, we need to first evaluate the logarithm log4 5, then use the result to calculate the exponentiation 16^log4 5. The final value can be found by substituting the logarithm value into the exponentiation equation and evaluating it using a calculator or mathematical software.