Question

The approximate value of $3^{2.001}$, if log 3 = 1.0986 is

• A. 9.00898
• B. 9.0989
• C. 9.0898
• D. 9.00989

Answer 1

Answer: (D)

9.00989

Answer 2

We start with:

$$3^{2.001} = 3^2 \times 3^{0.001} = 9 \times 3^{0.001}$$

Using the property $a^x = e^{x \ln a}$:

$$3^{0.001} = e^{0.001 \ln 3} \quad \text{with} \quad \ln 3 = 1.0986$$ $$3^{0.001} = e^{0.0010986} \approx 1 + 0.0010986 \quad \text{(using } e^x \approx 1+x \text{ for small } x\text{)}$$

Thus:

$$3^{2.001} \approx 9 \times (1 + 0.0010986) = 9 \times 1.0010986 \approx 9.00989$$