Precalculus 12 grade

Question

Solve for the exact value of x

log(5x-11)=log(9x+6)

Answer 1

If log(5x - 11) = log(9x + 6), then 5x - 11 = 9x + 6.

Solve for x.

Answer 2

4x= -17

x=-17/4 = -4.25

but impossible

as no logs are defined for negative values

no real solution

Answer 3

The equation log(5x - 11) = log(9x + 6) is well defined only if the logs are defined: their arguments must be positive, as there is no such thing as the logarithm of a negative number.

So we need 5x - 11 >0 and 9x + 6 >0 (simultaneously) ⇒ x > 11/5

With this is mind, we can solve the equation:

log(5x - 11) = log(9x + 6)

5x - 11 = 9x + 6

x = -17/4

which does not satisfy x > 11/5. So the equation has no solution