Question

Use logarithmic notation to represent the solution to each of the following equations. If there is 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(x) = 9^x has inverse function g(x) = log_9(x), so to solve an equation like 9^x = 10, use log_9(x) in this question. This question emphasizes that b^x and log_b(x) are inverses. a. 6^x = 58 x = log_6 (58) b. 6^x = 1/1296 x = -4 c. 4^x = - 73 x = DNE Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

          Use logarithmic notation to represent the solution to each of the following equations. If there is 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(x) = 9^x has inverse function g(x) = log_9(x), so to solve an equation like 9^x = 10, use log_9(x) in this question. This question emphasizes that b^x and log_b(x) are inverses.

a. 6^x = 58
   x = log_6 (58)

b. 6^x = 1/1296
   x = -4

c. 4^x = - 73
   x = DNE

Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

Use logarithmic notation to represent the solution to each of the following equations. If there is 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(x) = 9^x has inverse function g(x) = log9(x), so to solve an equation like 9^x = 10, use log9(x) in this question. This question emphasizes that b^x and logb(x) are inverses.

a. 6^x = 58
x = log6 (58)

b. 6^x = 1/1296
x = -4

c. 4^x = - 73
x = DNE

Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

Added by Taylor R.

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