Simplify log101.5 + 3 log102 − log100.3

To simplify the expression $\log_{10} 1.5 + 3 \log_{10} 2 - \log_{10} 0.3$, we will use the fundamental laws of logarithms.

1. Analyze the expression

The expression is: $\log_{10} 1.5 + 3 \log_{10} 2 - \log_{10} 0.3$

2. Explain the concepts

We need three key logarithm laws:

• Power Law: $n \log_a x = \log_a (x^n)$
• Addition Law: $\log_a x + \log_a y = \log_a (x \cdot y)$
• Subtraction Law: $\log_a x - \log_a y = \log_a (\frac{x}{y})$

3. Step-by-step solution

Step 1: Apply the Power Law to the middle term $3 \log_{10} 2 = \log_{10} (2^3) = \log_{10} 8$ Now the expression becomes: $\log_{10} 1.5 + \log_{10} 8 - \log_{10} 0.3$

Step 2: Apply the Addition Law $\log_{10} 1.5 + \log_{10} 8 = \log_{10} (1.5 \times 8)$ $1.5 \times 8 = 12$ So, the expression is now: $\log_{10} 12 - \log_{10} 0.3$

Step 3: Apply the Subtraction Law $\log_{10} 12 - \log_{10} 0.3 = \log_{10} (\frac{12}{0.3})$

To divide $12$ by $0.3$: $\frac{12}{0.3} = \frac{120}{3} = 40$

Therefore, the simplified expression is: $\log_{10} 40$

4. Identify the answer

Comparing our result to the given options: A. $\log_{10} 4$ B. $\log_{10} 40$ C. $\log_{10} -40$ D. $\log_{10} 4-$

The correct option is B.

5. Exam Tip

When dealing with logarithms in JAMB, always look to clear the coefficients (the numbers in front of the log) by moving them as exponents first. Also, remember that decimal division is easier if you multiply both the numerator and denominator by 10 or 100 to remove the decimal point!