Precalculus Examples

$\log (x) = - 2.1$

Step 1

Rewrite $\log (x) = - 2.1$ 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 $b^{y} = x$ .

$10^{- 2.1} = x$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $x = 10^{- 2.1}$ .

$x = 10^{- 2.1}$

Step 2.2

Simplify $10^{- 2.1}$ .

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Step 2.2.1

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

$x = \frac{1}{10^{2.1}}$

Step 2.2.2

Raise $10$ to the power of $2.1$ .

$x = \frac{1}{125.89254117}$

Step 2.2.3

Divide $1$ by $125.89254117$ .

$x = 0.00794328$