Given the exponential equation 5x = 0.3, which of the following would be a reasonable answer and why?
A. -7
B. -0.7
C. 0.7
D. 7
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Correct! -0.7 is the solution to the exponential equation. We know that x has to be negative because 0.3< 1. Then looking at the negative choices A and B, we can use our knowledge to eliminate A because 5-7 is a number that is almost zero and a lot less than 0.3. 5(-7) = 1/57 = 1/78125 = 0.0000128
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Problem 2:
Given the exponential equation 2x = 18, which number is the solution closer to?
A. 2
B. 3
C. 4
D. 5
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Correct! Using logic and reason, we know that 24 = 16 and 25 = 32 and since 18 is closer to 16 than 32 we know that the solution would be closer to 4 than to 5.
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Problem 3:
Given log x + log (x - 3) = 1, which of the following is not a reasonable solution?
A. -2
B. 5
C. -1
D. 3
Solving this problem, you get x = 5 and x = -2. Since you cannot take a log of a negative number to get a real solution, -2 is an extraneous solution.