Precalculus Examples

$- \log (x) = 5.1$

Step 1

Divide each term in $- \log (x) = 5.1$ by $- 1$ and simplify.

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Step 1.1

Divide each term in $- \log (x) = 5.1$ by $- 1$ .

$\frac{- \log (x)}{- 1} = \frac{5.1}{- 1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

$\frac{\log (x)}{1} = \frac{5.1}{- 1}$

Step 1.2.2

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

$\log (x) = \frac{5.1}{- 1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $5.1$ by $- 1$ .

$\log (x) = - 5.1$

Step 2

Rewrite $\log (x) = - 5.1$ 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 $b^{y} = x$ .

$10^{- 5.1} = x$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $x = 10^{- 5.1}$ .

$x = 10^{- 5.1}$

Step 3.2

Simplify $10^{- 5.1}$ .

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Step 3.2.1

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

$x = \frac{1}{10^{5.1}}$

Step 3.2.2

Raise $10$ to the power of $5.1$ .

$x = \frac{1}{125892.54117941}$

Step 3.2.3

Divide $1$ by $125892.54117941$ .

$x = 0.00000794$