Finite Math Examples

$\log_{5} (7 - 2 x) = 3 \log_{5} (2)$

Step 1

Simplify $3 \log_{5} (2)$ by moving $3$ inside the logarithm.

$\log_{5} (7 - 2 x) = \log_{5} (2^{3})$

Step 2

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

$7 - 2 x = 2^{3}$

Step 3

Solve for $x$ .

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Step 3.1

Raise $2$ to the power of $3$ .

$7 - 2 x = 8$

Step 3.2

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

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Step 3.2.1

Subtract $7$ from both sides of the equation.

$- 2 x = 8 - 7$

Step 3.2.2

Subtract $7$ from $8$ .

$- 2 x = 1$

Step 3.3

Divide each term in $- 2 x = 1$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 x = 1$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{1}{- 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{1}{- 2}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{- 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$