SOLUTION: 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.)

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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): You can put this solution on YOUR website!





...write as , and as



....if log same, then











=> exact solution

...round it

=> approximate solution





Answer by ikleyn(52776)   (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.

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