Algebra Examples

$\log (- 4 k) = \log (3 k + 10)$

Step 1

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

$- 4 k = 3 k + 10$

Step 2

Solve for $k$ .

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Step 2.1

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

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Step 2.1.1

Subtract $3 k$ from both sides of the equation.

$- 4 k - 3 k = 10$

Step 2.1.2

Subtract $3 k$ from $- 4 k$ .

$- 7 k = 10$

Step 2.2

Divide each term in $- 7 k = 10$ by $- 7$ and simplify.

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Step 2.2.1

Divide each term in $- 7 k = 10$ by $- 7$ .

$\frac{- 7 k}{- 7} = \frac{10}{- 7}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 7$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 7 k}{- 7} = \frac{10}{- 7}$

Step 2.2.2.1.2

Divide $k$ by $1$ .

$k = \frac{10}{- 7}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Move the negative in front of the fraction.

$k = - \frac{10}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{10}{7}$

Decimal Form:

$k = - 1.\overline{428571}$

Mixed Number Form:

$k = - 1 \frac{3}{7}$