Question 1206924: Algebraically solve
log(9x + 4) = 5 + log(2x − 6)
for x. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20849)   (Show Source):
Answer by ikleyn(52775)  (Show Source):
You can put this solution on YOUR website! .
Be careful ( ! )
In her post, @MathLover1 calls x= 3 as an approximate solution.
It is NOT SO.
In opposite, x=3 is a PROHIBITED value, which makes the argument of log(2x-6) equal to zero !
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
Algebraically solve
log(9x + 4) = 5 + log(2x − 6)
for x. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
 ----- Converting to EXPONENTIAL form
100,000(2x - 6) = 9x + 4 ----- Cross-multiplying
200,000x - 600,000 = 9x + 4
200,000x - 9x = 4 + 600,000
199,991x = 600,004
As stated by tutor @IKLEYN, 3 is NOT a solution because 3 will result in log (2x - 6) being log (0),
which is UNDEFINED. So, x MUST be > 3, and that's why x is ROUNDED to 6 decimal places, above.
GOT IT?
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