Solving Equations using Properties of Logarithms Answers
[___] x2 − 15 = 2x
Addition Property of Equality
[___] x − 5 = 0 or x + 3 = 0
Zero Product Property
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⇒ 2
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Which is the only solution to the equationlog3(x2 + 6x) = log3(2x + 12)?
Which shows the first step in the solution to the equation log2x + log2(x – 6) = 4?
What are the solutions tolog3x + log3(x2 + 2) = 1 + 2log3x?
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Insufficient information
x2 − 2x − 15 = 0 Potential solutions are −3 and 5 x2 − 15 = 2x x − 5 = 0 or x + 3 = 0 (x − 5)(x + 3) = 0
Question text not available
Which is the only solution to the equationlog3(x2 + 6x) = log3(2x + 12)?
Which shows the first step in the solution to the equation log2x + log2(x – 6) = 4?
What are the solutions tolog3x + log3(x2 + 2) = 1 + 2log3x?
x = or x =
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
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.
[___] Potential solutions are −3 and 5
Potential solutions
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