Chemistry Examples

$4.5 = - \log (H)$

Step 1

Rewrite the equation as $- \log (H) = 4.5$ .

$- \log (H) = 4.5$

Step 2

Divide each term in $- \log (H) = 4.5$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \log (H) = 4.5$ by $- 1$ .

$\frac{- \log (H)}{- 1} = \frac{4.5}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\log (H)}{1} = \frac{4.5}{- 1}$

Step 2.2.2

Divide $\log (H)$ by $1$ .

$\log (H) = \frac{4.5}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $4.5$ by $- 1$ .

$\log (H) = - 4.5$

Step 3

Rewrite $\log (H) = - 4.5$ 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 $b^{y} = x$ .

$10^{- 4.5} = H$

Step 4

Solve for $H$ .

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Step 4.1

Rewrite the equation as $H = 10^{- 4.5}$ .

$H = 10^{- 4.5}$

Step 4.2

Simplify $10^{- 4.5}$ .

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Step 4.2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$H = \frac{1}{10^{4.5}}$

Step 4.2.2

Raise $10$ to the power of $4.5$ .

$H = \frac{1}{31622.77660168}$

Step 4.2.3

Divide $1$ by $31622.77660168$ .

$H = 0.00003162$