Solving Equations using Properties of Logarithms…

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Solve the equation log4(x + 20) = 3x =

Answer:

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Solve the equation log6(13 – x) = 1.x =

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Answers:

x2 − 2x − 15 = 0:"2"

Potential solutions are −3 and 5:5

x2 − 15 = 2x:1

x − 5 = 0 or x + 3 = 0:4

(x − 5)(x + 3) = 0:3

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Answers:

Blank 1:-3

Blank 2:3

Find the potential solution to the equationlog4(2 – x) = log4(–5x – 18).x =

Answer:

-5

Which statement is true about the potential solution x = –5?

This number is not a true solution because it is negative.

This number is not a true solution because –5x – 18 is negative.

This number is not a true solution because 2 – x is negative.

This number is a true solution of the original equation.

Which is the only solution to the equationlog3(x2 + 6x) = log3(2x + 12)?

x = –6

x = –2

x = 0

x = 2

x = 6

Which shows the first step in the solution to the equation log2x + log2(x – 6) = 4?

log2[x(x – 6)] = 4

x + x – 6 = 4

x + x – 6 = 24

Option

The solution to the equation log2x + log2(x – 6) = 4 is x = .

Answer:

What are the solutions tolog3x + log3(x2 + 2) = 1 + 2log3x?

x = –2

x = –1

x = 1

x = 2

There is no true solution.

List the potential solutions to 2log x − log3 = log3 from least to greatest. x = or x =

Answers:

Blank 1:"-3"

Blank 2:3

Both are extraneous solutions.Only 3 is an extraneous solution. Only –3 is an extraneous solution. Neither is an extraneous solution.

Both are extraneous solutions.

Only 3 is an extraneous solution.

Only –3 is an extraneous solution.

Neither is an extraneous solution.

Explain the error in the solution below. What additional step needs to be completed?log x – log53 = 2log53 log x = 3log53 log x = log533 x = 27

Answer:

The error in the solution is treating the logarithms as if they have the same base. The first term, log x, is a common logarithm (base 10), while the other terms have a base of 5. The one-to-one property of logarithms only applies when the bases are identical. To solve the equation correctly, you must first use the change-of-base formula to rewrite the logarithms so they have the same base before attempting to equate the arguments.

Which of the following did you include in your response?

The bases of the logarithms are not the same.

The one-to-one property does not apply when the bases are not the same.

The change of base formula should have been used to write the logarithms with the same base.

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Which equation can you solve to find the potential solutions to the equation log2x + log2(x – 6) = 4?

x2 – 6x – 4 = 0

x2 – 6x – 8 = 0

x2 – 6x – 16 = 0

What is the solution to log7(x – 4) = log7(4x + 5) ?

x = –3