The expression shown in the image is:

$^2\log 16 - ^3\log 27 + ^5\log 1$

Let's break this down:

1. $^2\log 16$: This represents the logarithm of 16 with base 2. We know: $^2\log 16 = \log_2 16 = 4$ because $2^4 = 16$.

2. $^3\log 27$: This represents the logarithm of 27 with base 3. We know: $^3\log 27 = \log_3 27 = 3$ because $3^3 = 27$.

3. $^5\log 1$: The logarithm of 1 in any base is always 0: $^5\log 1 = \log_5 1 = 0$

Now, let's put everything together: $4 - 3 + 0 = 1$

The final result of the expression is 1.

Would you like any further explanation or details?

Here are some related questions for practice:

1. How do you simplify logarithmic expressions with different bases?
2. What is the logarithm of a number in base 10?
3. How can you convert between logarithms of different bases?
4. What is the change of base formula for logarithms?
5. How does logarithmic behavior affect exponential growth?

Tip: Remember that logarithms and exponents are inverse operations—this can help simplify many types of problems.