Pre-Algebra Examples

$5 \cdot 10^{x} = 0.005$

Step 1

Divide each term in $5 \cdot 10^{x} = 0.005$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 \cdot 10^{x} = 0.005$ by $5$ .

$\frac{5 \cdot 10^{x}}{5} = \frac{0.005}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 \cdot 10^{x}}{5} = \frac{0.005}{5}$

Step 1.2.1.2

Divide $10^{x}$ by $1$ .

$10^{x} = \frac{0.005}{5}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0.005$ by $5$ .

$10^{x} = 0.001$

Step 2

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

$\log (10^{x}) = \log (0.001)$

Step 3

Expand the left side.

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Step 3.1

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

$x \log (10) = \log (0.001)$

Step 3.2

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

$x \cdot 1 = \log (0.001)$

Step 3.3

Multiply $x$ by $1$ .

$x = \log (0.001)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \log (0.001)$

Decimal Form:

$x = - 3$