Finite Math Examples

$5 = 2 \cdot 10^{t}$

Step 1

Rewrite the equation as $2 \cdot 10^{t} = 5$ .

$2 \cdot 10^{t} = 5$

Step 2

Divide each term in $2 \cdot 10^{t} = 5$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 \cdot 10^{t} = 5$ by $2$ .

$\frac{2 \cdot 10^{t}}{2} = \frac{5}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 \cdot 10^{t}}{2} = \frac{5}{2}$

Step 2.2.1.2

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

$10^{t} = \frac{5}{2}$

Step 3

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

$\log (10^{t}) = \log (\frac{5}{2})$

Step 4

Expand the left side.

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Step 4.1

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

$t \log (10) = \log (\frac{5}{2})$

Step 4.2

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

$t \cdot 1 = \log (\frac{5}{2})$

Step 4.3

Multiply $t$ by $1$ .

$t = \log (\frac{5}{2})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \log (\frac{5}{2})$

Decimal Form:

$t = 0.39794000 \dots$