Solve for R R=2/3( log of E/(10^4.40))

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

Step 1

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

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

Step 2

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

Rewrite $\frac{E}{10^{4.4}}$ as $E {(10^{4.4})}^{- 1}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

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

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

Use logarithm rules to move $4.4 \cdot - 1$ out of the exponent.

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

Multiply $4.4$ by $- 1$ .

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

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

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

Multiply $- 4.4$ by $1$ .

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

Apply the distributive property.

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

Simplify $\frac{2}{3} \log (E)$ by moving $\frac{2}{3}$ inside the logarithm.

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

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

Combine $\frac{2}{3}$ and $- 4.4$ .

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

Multiply $2$ by $- 4.4$ .

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

Divide $- 8.8$ by $3$ .

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