Evaluate Log28 + Log216 - Log24

Analysis

The question requires the application of the laws of logarithms to simplify a single expression. Specifically, we will use the Product Law and the Quotient Law of logarithms.

Concept

The laws of logarithms state that for any base $a$:

1. Product Law: $\log_a(x) + \log_a(y) = \log_a(x \cdot y)$
2. Quotient Law: $\log_a(x) - \log_a(y) = \log_a\left(\frac{x}{y}\right)$

Step-by-Step Solution

Step 1: Apply the Product Law to the first two terms The expression is: $\log_2(8) + \log_2(16) - \log_2(4)$

Combine the first two terms: $\log_2(8 \times 16) - \log_2(4)$ $\log_2(128) - \log_2(4)$

Step 2: Apply the Quotient Law Now, combine the remaining terms: $\log_2\left(\frac{128}{4}\right)$ $\log_2(32)$

Step 3: Evaluate the logarithm We need to find the power to which $2$ must be raised to get $32$. $2^1 = 2$ $2^2 = 4$ $2^3 = 8$ $2^4 = 16$ $2^5 = 32$

Therefore, $\log_2(32) = 5$.

Conclusion

The calculation leads us to the value of 5, which corresponds to option C.

Exam Tip

When dealing with logarithms in JAMB, always look to simplify the numbers into powers of the base first (e.g., $8=2^3$, $16=2^4$, $4=2^2$). You can then use the power rule $\log_a(x^n) = n \log_a(x)$ to solve it even faster!