Question

If ln(a) = 2, ln(b) = 3, and ln(c) = 5, evaluate the following: (a) ln(a⁻³/b⁻⁴c⁻⁴), (b) ln(√(b⁻⁴c³a⁻²)), (c) (frac

Answer 1

To evaluate these expressions, we use logarithmic properties. The values for ln(a), ln(b), and ln(c) are given. We substitute these values into the expressions and simplify to find the values.

Step-by-step explanation:

To evaluate the given expressions, we can make use of logarithmic properties.

(a) ln(a⁻³/b⁻⁴c⁻⁴) = -3ln(a) - (-4ln(b) - 4ln(c)) = -3(2) - (-4(3) - 4(5)) = -6 + 12 + 20 = 26

(b) ln(√(b⁻⁴c³a⁻²)) = 1/2 ln(b⁻⁴c³a⁻²) = 1/2 (-4ln(b) + 3ln(c) - 2ln(a)) = 1/2 (-4(3) + 3(5) - 2(2)) = 1/2 (-12 + 15 - 4) = 1/2 (-16) = -8

(c) (a/b) / (c⁄a) = (a/a)(1/c)/b = 1/cb

Learn more about Logarithmic Properties