Question
Asked Dec 9, 2019
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Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer.
log 2(x+ 12) - log 2(x- 3) = 4
Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution set is {
(Simplify your answer. Use a comma to separate answers as needed.)
B. There are infinitely many solutions.
C. There is no solution.
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Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. log 2(x+ 12) - log 2(x- 3) = 4 Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is { (Simplify your answer. Use a comma to separate answers as needed.) B. There are infinitely many solutions. C. There is no solution.

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Expert Answer

Step 1

Given the logarithmic equation

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log, (x+12) – log, (x – 3)= 4

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Step 2

Simplify as follows.

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log, (x +12)– log,2(x- 3)=4 log, (x+12) = 4 + log, (x – 3) %3D log, (x +12) = log, (16) + log, (x – 3) |: 4= log, (2') = log, (16) | [: log. (a) + log. (b) = log. (ab)] log, (x +12)= log, (16(x – 3)) %3D

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Step 3

Using one-to-one property o...

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x+12 =16(x– 3) x+12 = 16x – 48 х—16х — —48-12 -15x = -60 х

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Tagged in

Math

Algebra

Logarithms