Precalculus Examples

$10^{x} = 0.1$

Step 1

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{x}) = \log (0.1)$

Step 2

Expand the left side.

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Step 2.1

Expand $\log (10^{x})$ by moving $x$ outside the logarithm.

$x \log (10) = \log (0.1)$

Step 2.2

Logarithm base $10$ of $10$ is $1$ .

$x \cdot 1 = \log (0.1)$

Step 2.3

Multiply $x$ by $1$ .

$x = \log (0.1)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \log (0.1)$

Decimal Form:

$x = - 1$