Precalculus Examples

$5.8 = - \log (x)$

Step 1

Rewrite the equation as $- \log (x) = 5.8$ .

$- \log (x) = 5.8$

Step 2

Divide each term in $- \log (x) = 5.8$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \log (x) = 5.8$ by $- 1$ .

$\frac{- \log (x)}{- 1} = \frac{5.8}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\log (x)}{1} = \frac{5.8}{- 1}$

Step 2.2.2

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

$\log (x) = \frac{5.8}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $5.8$ by $- 1$ .

$\log (x) = - 5.8$

Step 3

Rewrite $\log (x) = - 5.8$ 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 $b^{y} = x$ .

$10^{- 5.8} = x$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $x = 10^{- 5.8}$ .

$x = 10^{- 5.8}$

Step 4.2

Simplify $10^{- 5.8}$ .

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Step 4.2.1

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

$x = \frac{1}{10^{5.8}}$

Step 4.2.2

Raise $10$ to the power of $5.8$ .

$x = \frac{1}{630957.34448019}$

Step 4.2.3

Divide $1$ by $630957.34448019$ .

$x = 0.00000158$