Solve the following logarithmic equation. Express your answer as either an exact expression or a decimal approximation rounded to four decimal places. If there is no solution, indicate "No Solution (∅)."

log_7(x−5) + log_7(x+3) = log_7(x−2)

If you wish to enter log or ln, you must use the keypad. If there is more than one solution, separate your answers with a comma.

Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used.

x = ____________________ No Solution (∅)

Question

Solve the following logarithmic equation. Express your answer as either an exact expression or a decimal approximation rounded to four decimal places. If there is no solution, indicate "No Solution (∅)."

log_7(x−5) + log_7(x+3) = log_7(x−2)

If you wish to enter log or ln, you must use the keypad. If there is more than one solution, separate your answers with a comma.

Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used.

x = ____________________          No Solution (∅)

KyledaGreat · Answer

@vocaloid

KyledaGreat · Answer

is my answer right with $$x = \frac{ 3+\sqrt{61} }{ 2}$$

AZ · Answer

(x-5)(x+3) = x-2

x^2 - 2x - 15 = x - 2
x^2 - 3x - 13 = 0

and the only positive solution is the one you listed so good job!