Algebra Examples

R = \frac{2}{3} (\log (\frac{E}{10^{4.4}}))

$R = \frac{2}{3} (\log (\frac{E}{10^{4.4}}))$

Step 1

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\log (\frac{E}{10^{4.4}})

$\log (\frac{E}{10^{4.4}})$ .

R = \frac{2}{3} \cdot \log (\frac{E}{10^{4.4}})

$R = \frac{2}{3} \cdot \log (\frac{E}{10^{4.4}})$

Step 2

Simplify

\frac{2}{3} \cdot \log (\frac{E}{10^{4.4}})

$\frac{2}{3} \cdot \log (\frac{E}{10^{4.4}})$ .

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Step 2.1

Rewrite

\frac{E}{10^{4.4}}

$\frac{E}{10^{4.4}}$ as

E {(10^{4.4})}^{- 1}

$E {(10^{4.4})}^{- 1}$ .

R = \frac{2}{3} \cdot \log (E {(10^{4.4})}^{- 1})

$R = \frac{2}{3} \cdot \log (E {(10^{4.4})}^{- 1})$

Step 2.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

R = \frac{2}{3} \cdot \log (E \cdot 10^{4.4 \cdot - 1})

$R = \frac{2}{3} \cdot \log (E \cdot 10^{4.4 \cdot - 1})$

Step 2.3

Rewrite

\log (E \cdot 10^{4.4 \cdot - 1})

$\log (E \cdot 10^{4.4 \cdot - 1})$ as

\log (E) + \log (10^{4.4 \cdot - 1})

$\log (E) + \log (10^{4.4 \cdot - 1})$ .

R = \frac{2}{3} \cdot (\log (E) + \log (10^{4.4 \cdot - 1}))

$R = \frac{2}{3} \cdot (\log (E) + \log (10^{4.4 \cdot - 1}))$

Step 2.4

Use logarithm rules to move

4.4 \cdot - 1

$4.4 \cdot - 1$ out of the exponent.

R = \frac{2}{3} \cdot (\log (E) + 4.4 \cdot - 1 \log (10))

$R = \frac{2}{3} \cdot (\log (E) + 4.4 \cdot - 1 \log (10))$

Step 2.5

Multiply

4.4

$4.4$ by

- 1

$- 1$ .

R = \frac{2}{3} \cdot (\log (E) - 4.4 \log (10))

$R = \frac{2}{3} \cdot (\log (E) - 4.4 \log (10))$

Step 2.6

Logarithm base

10

$10$ of

10

$10$ is

1

$1$ .

R = \frac{2}{3} \cdot (\log (E) - 4.4 \cdot 1)

$R = \frac{2}{3} \cdot (\log (E) - 4.4 \cdot 1)$

Step 2.7

Multiply

- 4.4

$- 4.4$ by

1

$1$ .

R = \frac{2}{3} \cdot (\log (E) - 4.4)

$R = \frac{2}{3} \cdot (\log (E) - 4.4)$

Step 2.8

Apply the distributive property.

R = \frac{2}{3} \log (E) + \frac{2}{3} \cdot - 4.4

$R = \frac{2}{3} \log (E) + \frac{2}{3} \cdot - 4.4$

Step 2.9

Simplify

\frac{2}{3} \log (E)

$\frac{2}{3} \log (E)$ by moving

\frac{2}{3}

$\frac{2}{3}$ inside the logarithm.

R = \log (E^{\frac{2}{3}}) + \frac{2}{3} \cdot - 4.4

$R = \log (E^{\frac{2}{3}}) + \frac{2}{3} \cdot - 4.4$

Step 2.10

Multiply

\frac{2}{3} \cdot - 4.4

$\frac{2}{3} \cdot - 4.4$ .

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Step 2.10.1

Combine

\frac{2}{3}

$\frac{2}{3}$ and

- 4.4

$- 4.4$ .

R = \log (E^{\frac{2}{3}}) + \frac{2 \cdot - 4.4}{3}

$R = \log (E^{\frac{2}{3}}) + \frac{2 \cdot - 4.4}{3}$

Step 2.10.2

Multiply

2

$2$ by

- 4.4

$- 4.4$ .

R = \log (E^{\frac{2}{3}}) + \frac{- 8.8}{3}

$R = \log (E^{\frac{2}{3}}) + \frac{- 8.8}{3}$

R = \log (E^{\frac{2}{3}}) + \frac{- 8.8}{3}

$R = \log (E^{\frac{2}{3}}) + \frac{- 8.8}{3}$

Step 2.11

Divide

- 8.8

$- 8.8$ by

3

$3$ .

R = \log (E^{\frac{2}{3}}) - 2.9\overline{3}

$R = \log (E^{\frac{2}{3}}) - 2.9\overline{3}$

R = \log (E^{\frac{2}{3}}) - 2.9\overline{3}

$R = \log (E^{\frac{2}{3}}) - 2.9\overline{3}$

Step 3

The result can be shown in multiple forms.

Scientific Notation:

R = \log (E^{\frac{2}{3}}) - 2.9\overline{3}

$R = \log (E^{\frac{2}{3}}) - 2.9\overline{3}$

Expanded Form:

R = - \infty

$R = - \infty$