Question

If ln(a) = 1.5 and ln(b) = 0.6, then what is the value of 5ln(a²b³)?

Answer 1

The value of 5ln(a²b³), given ln(a) = 1.5 and ln(b) = 0.6, can be found using logarithm rules and is 24.

Step-by-step explanation:

The question provided asks about evaluating an expression involving logarithms, specifically to find the value of 5ln(a²b³). Given that ln(a) = 1.5 and ln(b) = 0.6, we can manipulate these equations using properties of logarithms to find the desired result.

Let's break down the process step-by-step:

1. Apply the logarithm power rule: ln(x^n) = n * ln(x) to both variables a and b inside the logarithm.
2. Multiply these individual logarithms by their respective exponents from the original expression.
3. Combine the results using the logarithm product rule: ln(xy) = ln(x) + ln(y).
4. Finally, multiply the entire logarithm by 5, as specified in the expression.

This process will yield the final numerical value for the expression 5ln(a²b³).

Let's perform the calculations:

• Step 1: ln(a²b³) becomes 2ln(a) + 3ln(b) because of the power rule.
• Step 2: Replace ln(a) and ln(b) with their given values to get 2 * 1.5 + 3 * 0.6.
• Step 3: Perform the multiplication to obtain 3 + 1.8.
• Step 4: Add the results to get 4.8.
• Step 5: Multiply by 5 to get the final answer: 5 * 4.8 = 24.

The value of 5ln(a²b³) is 24.