Which of the following is closest to the solution to 3^x = 0.00015?

A. -25
Incorrect. The solution will be negative to create a reciprocal to obtain a solution close to zero but this number is too small.

B. -8
Correct!

C. 8
Incorrect. Three to the eighth power would be a large number instead of a number close to zero.

D. -5
Incorrect. The exponent is negative to create a reciprocal but this number isn’t small enough.

Find a reasonable solution for log x + log (x + 48) = 2.

A. -50 and 2
Incorrect. There is not a value for a negative logarithm.

B. 8
Incorrect. Check your equation. Remember it is a log base 10; therefore, the simplified equation equals 100.

C. 2
Correct!

D. 6
Incorrect. Check your equation. Remember it is a log base 10; therefore, the simplified equation equals 100.

Which of the following is a reasonable solution for 2^x ≤ 113.14?

A. 7.2
Incorrect. Check the product of 2 seven times. It will be too large.

B. 50
Incorrect. The variable is in the exponent.

C. 6.8
Correct!

D. 8.1
Incorrect. Check the product of 2 eight times. It will be too large.

Which of the following is not a reasonable solution for log₂ x + log₂ (x – 7) ≥ 3?

A. 8
Incorrect. This value makes the inequality true.

B. -1
Correct!

C. 10
Incorrect. This value makes the inequality true.

D. 14
Incorrect. This value makes the inequality true.

Sara would like to increase her $10,000 savings to at least $40,000. One option for her is to invest her savings at a compound interest rate of 12% per year. Decide a reasonable time for Sara to reach her goal of $40,000.

Use the formula:

A = P(1 + i)n

A. 4 years
Incorrect. Use logarithms to calculate an approximate date.

B. 10 years
Incorrect. Use logarithms to calculate an approximate date.

C. 20 years
Incorrect. Sara would make her goal but this is not a reasonable answer. Use logarithms to calculate an approximate date.

D. 13 years
Correct! Since Sara needed to make at least $40,000 it will take a little over 12 years.