Finite Math Examples

ln (10) ⎡ ⎢ ⎣ \begin{matrix} 1 & 10 & 2 7 & 3 & - 2 0 & 1 & 5 \end{matrix} ⎤ ⎥ ⎦

$\ln (10) [\begin{array}{c} 1 & 10 & 2 \\ 7 & 3 & - 2 \\ 0 & 1 & 5 \end{array}]$

Step 1

Multiply

ln (10)

$\ln (10)$ by each element of the matrix.

⎡ ⎢ ⎣ \begin{matrix} ln (10) \cdot 1 & ln (10) \cdot 10 & ln (10) \cdot 2 ln (10) \cdot 7 & ln (10) \cdot 3 & ln (10) \cdot - 2 ln (10) \cdot 0 & ln (10) \cdot 1 & ln (10) \cdot 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} \ln (10) \cdot 1 & \ln (10) \cdot 10 & \ln (10) \cdot 2 \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply

ln (10)

$\ln (10)$ by

1

$1$ .

⎡ ⎢ ⎣ \begin{matrix} ln (10) & ln (10) \cdot 10 & ln (10) \cdot 2 ln (10) \cdot 7 & ln (10) \cdot 3 & ln (10) \cdot - 2 ln (10) \cdot 0 & ln (10) \cdot 1 & ln (10) \cdot 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} \ln (10) & \ln (10) \cdot 10 & \ln (10) \cdot 2 \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.2

Multiply

ln (10) \cdot 10

$\ln (10) \cdot 10$ .

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Step 2.2.1

Reorder

ln (10)

$\ln (10)$ and

10

$10$ .

⎡ ⎢ ⎣ \begin{matrix} ln (10) & 10 \cdot ln (10) & ln (10) \cdot 2 ln (10) \cdot 7 & ln (10) \cdot 3 & ln (10) \cdot - 2 ln (10) \cdot 0 & ln (10) \cdot 1 & ln (10) \cdot 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} \ln (10) & 10 \cdot \ln (10) & \ln (10) \cdot 2 \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.2.2

Simplify

10 \cdot ln (10)

$10 \cdot \ln (10)$ by moving

10

$10$ inside the logarithm.

⎡ ⎢ ⎢ ⎣ \begin{matrix} ln (10) & ln (10^{10}) & ln (10) \cdot 2 ln (10) \cdot 7 & ln (10) \cdot 3 & ln (10) \cdot - 2 ln (10) \cdot 0 & ln (10) \cdot 1 & ln (10) \cdot 5 \end{matrix} ⎤ ⎥ ⎥ ⎦

$[\begin{array}{c} \ln (10) & \ln (10^{10}) & \ln (10) \cdot 2 \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

⎡ ⎢ ⎢ ⎣ \begin{matrix} ln (10) & ln (10^{10}) & ln (10) \cdot 2 ln (10) \cdot 7 & ln (10) \cdot 3 & ln (10) \cdot - 2 ln (10) \cdot 0 & ln (10) \cdot 1 & ln (10) \cdot 5 \end{matrix} ⎤ ⎥ ⎥ ⎦

$[\begin{array}{c} \ln (10) & \ln (10^{10}) & \ln (10) \cdot 2 \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.3

Raise

10

$10$ to the power of

10

$10$ .

⎡ ⎢ ⎣ \begin{matrix} ln (10) & ln (10000000000) & ln (10) \cdot 2 ln (10) \cdot 7 & ln (10) \cdot 3 & ln (10) \cdot - 2 ln (10) \cdot 0 & ln (10) \cdot 1 & ln (10) \cdot 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (10) \cdot 2 \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.4

Multiply

ln (10) \cdot 2

$\ln (10) \cdot 2$ .

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Step 2.4.1

Reorder

ln (10)

$\ln (10)$ and

2

$2$ .

⎡ ⎢ ⎣ \begin{matrix} ln (10) & ln (10000000000) & 2 \cdot ln (10) ln (10) \cdot 7 & ln (10) \cdot 3 & ln (10) \cdot - 2 ln (10) \cdot 0 & ln (10) \cdot 1 & ln (10) \cdot 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} \ln (10) & \ln (10000000000) & 2 \cdot \ln (10) \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.4.2

Simplify

2 \cdot ln (10)

$2 \cdot \ln (10)$ by moving

2

$2$ inside the logarithm.

⎡ ⎢ ⎢ ⎣ \begin{matrix} ln (10) & ln (10000000000) & ln (10^{2}) ln (10) \cdot 7 & ln (10) \cdot 3 & ln (10) \cdot - 2 ln (10) \cdot 0 & ln (10) \cdot 1 & ln (10) \cdot 5 \end{matrix} ⎤ ⎥ ⎥ ⎦

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (10^{2}) \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.5

Raise

$10$ to the power of

$2$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10) \cdot 7 & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.6

Multiply

$\ln (10) \cdot 7$ .

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Step 2.6.1

Reorder

$\ln (10)$ and

$7$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ 7 \cdot \ln (10) & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.6.2

Simplify

$7 \cdot \ln (10)$ by moving

$7$ inside the logarithm.

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10^{7}) & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.7

Raise

$10$ to the power of

$7$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (10) \cdot 3 & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.8

Multiply

$\ln (10) \cdot 3$ .

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Step 2.8.1

Reorder

$\ln (10)$ and

$3$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & 3 \cdot \ln (10) & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.8.2

Simplify

$3 \cdot \ln (10)$ by moving

$3$ inside the logarithm.

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (10^{3}) & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.9

Raise

$10$ to the power of

$3$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & \ln (10) \cdot - 2 \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.10

Multiply

$\ln (10) \cdot - 2$ .

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Step 2.10.1

Reorder

$\ln (10)$ and

$- 2$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & - 2 \cdot \ln (10) \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.10.2

Simplify

$- 2 \cdot \ln (10)$ by moving

$2$ inside the logarithm.

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & - \ln (10^{2}) \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.11

Raise

$10$ to the power of

$2$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & - \ln (100) \\ \ln (10) \cdot 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.12

Multiply

$\ln (10)$ by

$0$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & - \ln (100) \\ 0 & \ln (10) \cdot 1 & \ln (10) \cdot 5 \end{array}]$

Step 2.13

Multiply

$\ln (10)$ by

$1$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & - \ln (100) \\ 0 & \ln (10) & \ln (10) \cdot 5 \end{array}]$

Step 2.14

Multiply

$\ln (10) \cdot 5$ .

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Step 2.14.1

Reorder

$\ln (10)$ and

$5$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & - \ln (100) \\ 0 & \ln (10) & 5 \cdot \ln (10) \end{array}]$

Step 2.14.2

Simplify

$5 \cdot \ln (10)$ by moving

$5$ inside the logarithm.

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & - \ln (100) \\ 0 & \ln (10) & \ln (10^{5}) \end{array}]$

Step 2.15

Raise

$10$ to the power of

$5$ .

$[\begin{array}{c} \ln (10) & \ln (10000000000) & \ln (100) \\ \ln (10000000) & \ln (1000) & - \ln (100) \\ 0 & \ln (10) & \ln (100000) \end{array}]$