Building numbersense for logarithms by bounding them by integer values. For each of the following logarithmic expressions, give the two integers that its value falls between. The rst one is done for you. Hint: Remember that logarithms represent exponents. 1 1 1 a. The value of log3 (m) is greater than 4 and less than 3 because 3 '4 = a and 3 T 3 = E- b. The value of log5 (300) is greater than |:|x and less than |:|x . c. The value oflogm(97,902) is greater than |:|x and less than |:|x . 1 d. The value of log2 (W) is greater than :3: and less than |:|x . Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 3: Enter your answer as a number (like 5, 3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 4: Enter your answer as a number (like 5, 3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 5: Enter your answer as a number (like 5, 3, 2.2172) or as a calculation (like 5/3, 23, 5--4) Enter DNE for Does Not Exist, 00 for Innity Box 6: Enter your answer as a number (like 5, 3, 2.2172) or as a calculation (like 5/3, 2A3, 5--4) Enter DNE for Does Not Exist, 00 for Innity Submit Use logarithmic notation to represent the solution to each of the following equations. If there is no solution, enter "DNE". Professor Lapan's Helpful Hint: For this question, do not evaluate solutions numerically. Instead, choose logarithms that undo the given exponential function. For example, f(a:) = 91 has inverse function 9(3) 2 log9 (3:), so to solve an equation like 91 = 10, use log9(m) in this question. This question emphasizes that bm and 10gb(:c) are inverses. a 61 2 61 e : S Preview m 1 b. 6 216 e : Z Preview c 43 : 86 a: = ' Preview Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 23, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2A3, 5+4) Enter DNE for Does Not Exist, 00 for Innity Submit Rewrite each of the following exponential equations in logarithmic form. a. y : 9I |:] Preview b. v = 8(2.1)' |:] Preview c. b = 38\". Tip: Solve for a. Simplify your answer so that the base of the logarithm is a prime number and b contains no exponent. |:] Preview Box 1: Enter your answer as an equation, Example: F3x"2+l, 2+x+F3 Be sure your variables match those in the question Box 2: Enter your answer as an equation. Example: F3x"2+1, 2+x+y:3 Be sure your variables match those in the question Box 3: Enter your answer as an equation, Example: y=3x"2+1, 2+x+y=3 Be sure your variables match those in the question Submit Rewrite each of the following exponential equations in logarithmic form. a. y : 9I |:] Preview b. v = 8(2.1)' |:] Preview c. b = 38\". Tip: Solve for a. Simplify your answer so that the base of the logarithm is a prime number and b contains no exponent. |:] Preview Box 1: Enter your answer as an equation, Example: F3x"2+l, 2+x+F3 Be sure your variables match those in the question Box 2: Enter your answer as an equation. Example: F3x"2+1, 2+x+y:3 Be sure your variables match those in the question Box 3: Enter your answer as an equation, Example: y=3x"2+1, 2+x+y=3 Be sure your variables match those in the question Submit Solve each equation for the other variable. (Hint: This will involve rewriting each equation in exponential form at some step in the process.) ay=mea) Preview b. :1: : log3 (%) Preview Box 1: Enter your answer as an equation. Example: y=3x"2+l, 2+x+y23 Be sure your variables match those in the question Box 2: Enter your answer as an equation. Example: y=3x"2+1, 2+x+y=3 Be sure your variables match those in the question Submit For each of the following functions, write the formula for the function's inverse. a. f(x) = 5" where y = f(x). f -1(y ) = Preview b. f(x) = 3(2.8) where y = f(x). f -1 (y ) = Preview c. f(x) = log , where y = f(x). f -1 (y ) = Preview Box 1: Enter your answer as an expression. Example: 3x 2+1, x/5, (a+b)/c Be sure your variables match those in the question Box 2: Enter your answer as an expression. Example: 3x 2+1, x/5, (a+b)/c Be sure your variables match those in the question Box 3: Enter your answer as an expression. Example: 3x 2+1, x/5, (a+b)/c Be sure your variables match those in the question Submit Question 5. Points possible: 3 License Unlimited attempts. Without using a calculator, determine the values of the following expressions. (Hint: your answer should be a single number, not a calculation. a. log3 (9) = b. log2 (64) = c. log4 16Rewrite each of the following expressions as a single logarithm. That is, each answer should contain only one log (or In) expression. Assume x , y, z > 0. a. log2 (x) + log2(y) = Preview b. logs(2) - logs(y) = Preview c. 4logg (x) + logs(y) = Preview d. In(x) + In(y) - In(z) = Previewa. Which of the following expressions is equivalent to log(16)? Select all that apply and be careful! 04 . log (2) Olog(16) + log(0) Olog(20) - log(4) Olog(8) + log(2) 02 . log (4) b. Which of the following expressions is equivalent to In (10x2) assuming that x > 0. Select all that apply and be careful! OIn(20x3) - In(2x) 02 . In(a) + In(10) OIn(5x) + In(2x) OIn (40ac2) - In(4) 02 . In(10x) c. Which of the following expressions is equivalent to In (10x2) for all values of x, including x