Question

Given logᵩ2=0.33 and logᵩ5=0.77, calculate logᵩ40. (Hint: Expand using sums or differences of the factors 2 and 5 .)

Answer 1

To calculate logᵩ240, express 40 as a product of its prime factors (2³×5), and use the properties of logarithms to find that logᵩ240 is 1.76 using the given values for logᵩ22 and logᵩ25.

Step-by-step explanation:

The student is asking to calculate logᵩ240 using given values for logᵩ22 and logᵩ25. To find logᵩ240, we first express 40 as a product of its prime factors, which is 2³×5. By using the properties of logarithms:

• logᵩ2(2³×5) = logᵩ2(2³) + logᵩ2(5)
• logᵩ2(2³) = 3 × logᵩ2(2) = 3 × 0.33 = 0.99
• logᵩ2(40) = 0.99 + 0.77 = 1.76

Therefore, logᵩ240 is 1.76.