Solving Exponential and Logarithmic Equations

Question 1

Because the are equal

Revolt · Accepted Answer

A: bases

Question 2

What equation is equivalent to 9x - 3 = 729?

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B: 9x - 3 = 93

Question 3

To solve 5(2x + 4) = 15, first divide each side by .

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5

Question 4

Which of the following is the solution of 5e2x - 4 = 11?

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C: mc001-1.jpg

Question 5

Question 5

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A,E

Question 6

Question 6

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B

Question 7

What is the solution to ln (x2 - 16) = 0?

Revolt · Accepted Answer

A: mc001-1.jpg

Question 8

Solve: ln 2x + ln 2 = 0x =

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1/4

Question 9

Consider the equation log(3x - 1) = log28. Explain why 3x - 1 is not equal to 8. Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to.

Revolt · Accepted Answer

In the equation log(3x - 1) = log2(8), 3x - 1 is not equal to 8 because the logarithms have different bases; the left side is the common logarithm (base 10) while the right side is base 2. To solve the equation, first simplify the right side: log2(8) = 3 because 2 to the third power is 8. This results in the equation log(3x - 1) = 3. Next, rewrite the logarithmic equation in exponential form using base 10: 3x - 1 = 10^3. Therefore, 3x - 1 is equal to 1000. To find x, add 1 to both sides and divide by 3 (x = 1001/3).

Question 10

An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number. years

Revolt · Accepted Answer

8

Solving Exponential and Logarithmic Equations Answers

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