Question 33, 3.4.67
HW Score: $64.63 %, 26.5$ of 41 points
Points: 0 of 1
Solve the logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expressions. Give an exact answer.
$\log_{13} x + \log_{13} (12 x - 1) = 1$

Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Answer

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Answer

$x = \frac{13}{12}$

Steps

Step 1 ： $\log_{13} (x (12 x - 1)) = 1$

Step 2 ： $13^{1} = x (12 x - 1)$

Step 3 ： $13 = 12 x^{2} - x$

Step 4 ： $12 x^{2} - x - 13 = 0$

Step 5 ： $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Step 6 ： $x = \frac{1 \pm \sqrt{(- 1)^{2} - 4 * 12 * (- 13)}}{2 * 12}$

Step 7 ： $x = \frac{1 + \sqrt{625}}{24} = \frac{26}{24} = \frac{13}{12}$

Step 8 ： $x = \frac{1 - \sqrt{625}}{24} = - \frac{24}{24} = - 1$

Step 9 ： $x = \frac{13}{12}$