Finite Math Examples

$\log (10) x + \log (10) \cdot 3 = 2 \log (10) \cdot 4 - \log (10) \cdot 2$

Step 1

Simplify the expressions in the equation.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Move $3$ to the left of $\log (10)$ .

$\log (10) x + 3 \log (10) = 2 \log (10) \cdot 4 - \log (10) \cdot 2$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $2 \log (10) \cdot 4 - \log (10) \cdot 2$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Multiply $4$ by $2$ .

$\log (10) x + 3 \log (10) = 8 \log (10) - \log (10) \cdot 2$

Step 1.2.1.1.2

Multiply $2$ by $- 1$ .

$\log (10) x + 3 \log (10) = 8 \log (10) - 2 \log (10)$

Step 1.2.1.2

Subtract $2 \log (10)$ from $8 \log (10)$ .

$\log (10) x + 3 \log (10) = 6 \log (10)$

Step 2

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

$\log (10) x + 3 \log (10) - 6 \log (10) = 0$

Step 3

Simplify each term.

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Step 3.1

Logarithm base $10$ of $10$ is $1$ .

$1 x + 3 \log (10) - 6 \log (10) = 0$

Step 3.2

Multiply $x$ by $1$ .

$x + 3 \log (10) - 6 \log (10) = 0$

Step 3.3

Logarithm base $10$ of $10$ is $1$ .

$x + 3 \cdot 1 - 6 \log (10) = 0$

Step 3.4

Multiply $3$ by $1$ .

$x + 3 - 6 \log (10) = 0$

Step 3.5

Logarithm base $10$ of $10$ is $1$ .

$x + 3 - 6 \cdot 1 = 0$

Step 3.6

Multiply $- 6$ by $1$ .

$x + 3 - 6 = 0$

Step 4

Subtract $6$ from $3$ .

$x - 3 = 0$

Step 5

Add $3$ to both sides of the equation.

$x = 3$