Question

Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers. help (x – 4)^38 In (3x – 8)^34 (logarithms) Hint: vu? = (ul. (b) Use your answer from part to evaluate the derivative. d/dx In (x – 4)^38 (3x – 8)^34 = help 100 (formulas)

Answer 1

To write the expression (x – 4)³⁸ In (3x – 8)³⁴using sums and/or differences of logarithmic expressions, split the expression into two separate logarithmic expressions and apply the properties of logarithms. The expression can then be written as: 38 * log(x – 4) + 34 * log(3x – 8).

Step-by-step explanation:

To write the expression (x – 4)³⁸ In (3x – 8)³⁴ using sums and/or differences of logarithmic expressions, we can apply the properties of logarithms. We know that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers. Thus, we can split the expression into two separate logarithmic expressions:

(x – 4)³⁸ = 38 * log(x – 4)

(3x – 8)³⁴ = 34 * log(3x – 8)

Therefore, the expression can be written as: 38 * log(x – 4) + 34 * log(3x – 8).