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A set of logarithmic and exponential equations to be solved. The tasks include changing equations to logarithmic or exponential form, finding the number given a logarithm, solving for variables using logarithms, and determining the domain and range of functions. Some problems also require finding the x-intercept or expressing one function in terms of another.
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1.4.16/4.16 points Change to logarithmic form. (a) 53 = 125 (b) 5 โ^3 = 1 125 (c) t r^ = s (d) 3 x^ = 5 โ t (e) 57 t^ = a + b a (f) (0.5) t^ = 7. 2.4.16/4.16 points Change to exponential form. (a) log 3 81 = 4 (b) log 4 1 256 = โ 4 (c) log v w = q (d) log 4 (2 x โ 1) = 2 Practice Another Version
(e) log 4 p = 6 โ x (f) log a 343 = 4 5 3.4.16/4.16 points Change to exponential form. (a) log x = 80 (b) log x = 50 t (c) ln x = 0. (d) ln w = 5 + 4 x (e) ln( z โ 2) = 1 4 4.4.16/4.16 points Change to logarithmic form. (a) 105 = 100, (b) 10 โ^3 = 0. (c) 10 x^ = y โ 3 (e) e^5 = p (e) e^2 t^ = 3 โ x Practice Another Version Practice Another Version Practice Another Version
7.4.16/4.16 points Solve for x in each of the two equations below. IMPORTANT: You must give a symbolic, not decimal answer. Find logarithms in the Calcpad function drawer. Part 1: 10 x = 195 x = Part 2: e โ x /^9 = x = 8.4.16/4.16 points Solve the following equation for x: log 8 (6x + 1) = 5 IMPORTANT: Provide an exact expression, not a decimal approximation. x = Watch It 9.4.16/4.16 points Find all solutions of the equation ln( x^2 ) = 2 If there is only one solution, enter it in BOTH boxes below; If there are two solutions, enter the SMALLER solution in the first box and the LARGER solution in the second box. IMPORTANT: Provide exact expressions, not decimal approximations. 10.4.16/4.16 points Solve the equation. log 11 ( x ) = log 11 ( 8 โ 2 x ) Give an exact, not decimal answer. x = Practice Another Version Practice Another Version Practice Another Version Practice Another Version
11.4.16/4.16 points Solve the following equation for x: ln(3x - 6) = 5 IMPORTANT: Provide an exact expression, not a decimal approximation. x = 12.3.12/4.16 points Find the domain of the function f ( x ) = 2 โ e^8 x Select the proper symbol for each end of the intervals using the drop-down boxes, and enter the endpoints of the intervals in the blanks. If an endpoint is positive or negative infinity, use the CalcPad
domain: ( ( , ] ] 13.4.16/4.16 points Determine the domain and range of the function f ( x ) = ln( x โ 3 ).
domain: ( ( , ) ) range: ( ( , ) ) 14.4.16/4.16 points This question has two parts. Part 1: Find the domain of the function f(x) = 6 + ln(3x + 8). Enter your answer in interval notation. If an endpoint is positive or negative infinity, use the CalcPad
Domain: Part 2: Find the x-intercept of the function f. (Your answer is a number, not an ordered pair.) IMPORTANT: Provide an exact expression, not a decimal approximation. x-intercept: Watch It Practice Another Version Practice Another Version Practice Another Version Practice Another Version
f ( x ) = F (โ x ) f ( x ) = F ( x + 3) f ( x ) = โ F ( x ) f ( x ) = 2 F ( x ) 17.4.16/4.16 points Sketch the graph of f. f ( x ) = ln| x โ 2 |
18.โ/4.16 points You invest $7,400 at 5% per annum compounded continuously. Determine the time T (in years) for your investment to be worth $12,025. Enter an exact answer or round to two decimal places. Time required: T = years Practice Another Version
b^4 (โ6 b^5 )
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