hello can someone please help me with these calculus questions #8 is multiple choice. please help me understand along with proper solution thank you.

Problem #1: By simplifying the given expression on the left hand side of each equation, find the value of the question mark on the corresponding right hand side. 8 4 (- 1 - B =5 (=) = - | %(}t - a)O = (x- a)? Problem #1(a): Problem #1(b): Problem #1(c): Problem #2: By simplifying the expression on the left hand side of the following equation, find the values of a and b on the right hand side. -3/2 ( * 1/2 1 3/4 ) - 1 = x 0 yb Enter the values of a and b (in that order) into the answer box below, separated by a comma. Do not include 'a = ' or 'b = ' in your answer. e.g., 4,-7/2 Problem #2:Problem #3: Find all real numbers x that satisfy the given equation. @) 36* (2) = 36 (b) 427 =% = 16* 1 40 x2 6 (E) =4 Problem #3(a): Do not include "x =" in your answer. Problem #3(b): Problem #3(c): Problem #4: Find all values of the constants C and b such that the curve: y=Cb* passes through the points (4, 66) and (5, 198). Enter your answer symbolically, Problem #4: as in these examples Separate your answers with a comma, i.e., C, b Problem #5: Suppose that $2000 is invested at an annual interest rate of 8%. Compute the balance after 7 years if the interest is compounded (a) annually (b) semiannually () quarterly (d) continuously Problem #6: How much money should be invested now at 2% to obtain $17000 in 11 years if interest is compounded (a) quarterly? (b) continously? Problem #6(a): Round your answer to 2 decimals. Problem #6(b): Round your answer to 2 decimals. Problem #7: Find the effective interest rate 7 for investments with the following annual interest rates. Express your answer as a percentage, rounded to 2 decimals, and without the '%' sign (e.g., 8.79). (a) 3.55% compounded monthly (b) 3.53% compounded daily (using 365 days per year). () 3.49% compounded continuously Problem #8: Use the logarithmic rules to evaluate (i.e., expand) the following expression: X 115 In( 5 V1+x2 (A) -24 In x - - In(1 + x2) (B) 29 Inx (C) 26 Inx - } In(1 + x2) (D) -24 Inx + / In(1 + x2) (E) 21 Inx (F) 3 Inx (G) 26 Inx + , In(1 + x2) (H) Inx Problem #8: Select