Finite Math Examples

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

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

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

$3$ to the left of

log (10)

$\log (10)$ .

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

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

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

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

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

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

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Multiply

4

$4$ by

2

$2$ .

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

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

Step 1.2.1.1.2

Multiply

2

$2$ by

- 1

$- 1$ .

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

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

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

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

Step 1.2.1.2

Subtract

2 log (10)

$2 \log (10)$ from

8 log (10)

$8 \log (10)$ .

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

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

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

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

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

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

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

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

Step 3

Simplify each term.

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Step 3.1

Logarithm base

10

$10$ of

10

$10$ is

1

$1$ .

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

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

Step 3.2

Multiply

x

$x$ by

1

$1$ .

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

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

Step 3.3

Logarithm base

10

$10$ of

10

$10$ is

1

$1$ .

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

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

Step 3.4

Multiply

3

$3$ by

1

$1$ .

x + 3 - 6 log (10) = 0

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

Step 3.5

Logarithm base

10

$10$ of

10

$10$ is

1

$1$ .

x + 3 - 6 \cdot 1 = 0

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

Step 3.6

Multiply

- 6

$- 6$ by

1

$1$ .

x + 3 - 6 = 0

$x + 3 - 6 = 0$

x + 3 - 6 = 0

$x + 3 - 6 = 0$

Step 4

Subtract

6

$6$ from

3

$3$ .

x - 3 = 0

$x - 3 = 0$

Step 5

Add

3

$3$ to both sides of the equation.

x = 3

$x = 3$