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 (∅)

Answer 1

@vocaloid

Answer 2

any idea?

Answer 3

log m+log n=log mn
\[\log_{7} (x-5)+\log_{7} (x+3)=\log_{7} (x-2)\]
\[\log_{7} (x-5)(x+3)=\log_{7} (x-2)\]
x-5>0,x>5
x+3>0,x>-3
x-2>0,x>2
combining
x>5
also
(x-5)(x+3)=x-2
\[x^2-5x+3x-15-x+2=0\]
\[x^2-3x-13=0\]
solve for x
remember x>5