Precalculus Examples

$\log_{19} (8 - 3 a) = \log_{19} (- 4 a - 10)$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$8 - 3 a = - 4 a - 10$

Step 2

Solve for $a$ .

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Step 2.1

Move all terms containing $a$ to the left side of the equation.

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Step 2.1.1

Add $4 a$ to both sides of the equation.

$8 - 3 a + 4 a = - 10$

Step 2.1.2

Add $- 3 a$ and $4 a$ .

$8 + a = - 10$

Step 2.2

Move all terms not containing $a$ to the right side of the equation.

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Step 2.2.1

Subtract $8$ from both sides of the equation.

$a = - 10 - 8$

Step 2.2.2

Subtract $8$ from $- 10$ .

$a = - 18$