Lesya P.

asked • 01/11/24

Precalculus 12 grade

Solve for the exact value of x

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

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Mark M. answered • 01/11/24

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


Solve for x.


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Josh F.

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Yes to the above, and be sure to check the solution you get by substituting for x in the original equation because if that value for x makes the arguments of the log (ie the number inside the log) negative, it is an extraneous (invalid) solution. In that case, there are no solutions.
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01/11/24

Lesya P.

x=-17/4 TELL IS CORRECT. Tell solve for x. it is no SOLUTATION for equation.
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01/11/24

Mark M.

tutor
If x = -17/4 , then 5x - 11 is negative. So, log(5x - 11) is undefined. Therefore, the equation log(5x - 11) = log(9x+6) has NO SOLUTION.
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01/12/24

Lorenzo B. answered • 01/12/24

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5.0 (32)

Physics MS, Rice U Chemistry PhD, passionate Physics and Math Tutor
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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

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