Chemistry Examples

$3.5 = - \log (H_{3} O)$

Step 1

Since $H_{3}$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- \log (H_{3} O) = 3.5$

Step 2

Divide each term in $- \log (H_{3} O) = 3.5$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \log (H_{3} O) = 3.5$ by $- 1$ .

$\frac{- \log (H_{3} O)}{- 1} = \frac{3.5}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\log (H_{3} O)}{1} = \frac{3.5}{- 1}$

Step 2.2.2

Divide $\log (H_{3} O)$ by $1$ .

$\log (H_{3} O) = \frac{3.5}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $3.5$ by $- 1$ .

$\log (H_{3} O) = - 3.5$

Step 3

Rewrite $\log (H_{3} O) = - 3.5$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{- 3.5} = H_{3} O$

Step 4

Solve for $H_{3}$ .

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Step 4.1

Rewrite the equation as $H_{3} O = 10^{- 3.5}$ .

$H_{3} O = 10^{- 3.5}$

Step 4.2

Divide each term in $H_{3} O = 10^{- 3.5}$ by $O$ and simplify.

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Step 4.2.1

Divide each term in $H_{3} O = 10^{- 3.5}$ by $O$ .

$\frac{H_{3} O}{O} = \frac{10^{- 3.5}}{O}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $O$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{H_{3} O}{O} = \frac{10^{- 3.5}}{O}$

Step 4.2.2.1.2

Divide $H_{3}$ by $1$ .

$H_{3} = \frac{10^{- 3.5}}{O}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify the expression.

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Step 4.2.3.1.1

Move $10^{- 3.5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$H_{3} = \frac{1}{O \cdot 10^{3.5}}$

Step 4.2.3.1.2

Raise $10$ to the power of $3.5$ .

$H_{3} = \frac{1}{O \cdot 3162.27766016}$

Step 4.2.3.1.3

Move $3162.27766016$ to the left of $O$ .

$H_{3} = \frac{1}{3162.27766016 \cdot O}$

Step 4.2.3.2

Rewrite $1$ as $1 (1)$ .

$H_{3} = \frac{1 (1)}{3162.27766016 \cdot O}$

Step 4.2.3.3

Factor $3162.27766016$ out of $3162.27766016 \cdot O$ .

$H_{3} = \frac{1 (1)}{3162.27766016 (O)}$

Step 4.2.3.4

Separate fractions.

$H_{3} = \frac{1}{3162.27766016} \cdot \frac{1}{O}$

Step 4.2.3.5

Divide $1$ by $3162.27766016$ .

$H_{3} = 0.00031622 \frac{1}{O}$

Step 4.2.3.6

Combine $0.00031622$ and $\frac{1}{O}$ .

$H_{3} = \frac{0.00031622}{O}$