Basic Math Examples

$10^{k - 2} = 20$

Step 1

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

$\log (10^{k - 2}) = \log (20)$

Step 2

Expand the left side.

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Step 2.1

Expand $\log (10^{k - 2})$ by moving $k - 2$ outside the logarithm.

$(k - 2) \log (10) = \log (20)$

Step 2.2

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

$(k - 2) \cdot 1 = \log (20)$

Step 2.3

Multiply $k - 2$ by $1$ .

$k - 2 = \log (20)$

Step 3

Add $2$ to both sides of the equation.

$k = \log (20) + 2$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \log (20) + 2$

Decimal Form:

$k = 3.30102999 \dots$