Solve the logarithmic equation. Be sure to reject any value of x that is not in

Question

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 log3(x + 21)-log3(x-5)=3 Rewrite the given equation without logarithms. Do not solve for x Solve the equation. Select the correct choice below and,i necessary, illin the answer box to complete your choice A. The solution set is (Simplify your answer. Use a comma to separate answers as needed.) O B. There are infinitely many solutions There is no solution. Click to select your answers) 207 PM

Explanation / Answer

Given equation, log3(x+21) - log3(x-5) = 3

i.e., log3[(x+21)/(x-5)] = 3

i.e., 3log3[(x+21)/(x-5)] = 33

i.e., (x+21)/(x-5) = 27

This is the form of the equation without logarithms.

Now, (x+21)/(x-5) = 27

i.e., x+21 = 27*(x-5)

i.e., x+21 = (27*x) - 135

i.e., x - (27*x) = -135 -21

i.e., -(26*x) = -156

i.e., x = (-156)/(-26)

i.e., x = 6

Hence, the solution of the given equation is 6.

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