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 (∅)."

Answer 1

\[\log _{_{3}}(x - 3) +\log _{3}(x + 6) = \log _{3}(5x - 10)\]

Answer 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 3

@vocaloid

Answer 4

is the answer 4 , something else, or no solution ?

Answer 5

You need to know some log properties:

\( \log (a) + \log(b) = \log(a\cdot b)\)

and

\( \log (x) = \log(y)\) means that
\( x = y\)

Answer 6

\(\log _{_{3}}(x - 3) +\log _{3}(x + 6) = \log _{3}(5x - 10)\)

First simplify the left side of the equation using the property I shared above.

What do you get?
Basically to combine the two logs being added, it's going to be the same as log of both terms being multiplied