Hello math Tutor,

Please help me how to answer all of them? i want it is handwriting and be detailed Thank you

1. Convert each exponential equation to a logarithmic equation. The logarithmic equation for part b should not include the square root sign. a. 25 = 32 b. 5 = Vx 2. Solve by converting to exponential form. (2 marks) a. log x = -3 b. log, (81) =4 3. Given the function f (x) = 3*+1 a. Graph f (x) and f (x) showing a minimum of two exact points for each function. Clearly label each curve and also show and label the line of reflection.b. Given f (x) =3* algebraically determine the equation for f (x). c. Describe the transformation using a mapping statement. 4. The function y = log, x is transformed to the function y = -3log2-= (x+1) )-4. a. Use the transformation statement y = a log. (b(x -h) ) + k to complete the chart below. Parameter |Mapping Statement |Transformation Description a =-3 (x, y) - (x,-3y) Vertical stretch by a factor of 3 and a reflection across the line y=0 (the x-axis). b = h = k =b. Sketch the graph of y = -3log2 -= (x+1) )-4.5. Laws of Logarithms 3. Use the laws of logarithms to express as a single logarithm and then evaluate . log2 6 log2 3 + 210g2 J5} b. Use the laws of logarithms to exnress as a sinele logarithm and then simplify. Also, determine the restriction for x. 210g5 (x3)1(:Ig5 (x2 x6) 6. .d'ltlgebraitzallyr determine the exact solution to 3" = 5\"1 7. Algebraically determine the exact solution to log3(x 4) = 2 log3 (x +4) 8. Keith makes an investment of $3000 paying at an interest rate of 7.5% per year, compounded quarterly. One form of the compound interest formula isA = Pa +1)" , where A is the amount of money at the end of the investment; P is the principal amount deposited; i is the interest rate per compounding period; and n is the number of compounding periods. Use the above formula to algebrdcally determine the number of compounding periods it would take for the investment to double. (Hint: Review page 362 in the textbook to help you set up this equatinn and than qnlup usin the logarithmic laws.) State your value fornto one decimal place. b. Explain why the correct solution for the number of compounding periods is 38 and not 37. Another form of the compound interest formula is A = P + , where A is the L)!!! n amount of money at the end of the investment; P is the principal amount deposited; r is the interest rate per year; It is the number of compounding periods a year; and 1' is the total time in years. Using this second formula graphically determine the time in years it would take for the investment to double. Show your work by completing the statements below for your graphing calculator steps. Explain how this answer verifies your results from part a. (Hint: There are 3 months in each compounding period.) y1: y2