Finite Math Examples

$t = - \frac{1}{0.0075} \cdot \ln (\frac{0.00004 - 0.5}{a (0.5)})$

Step 1

Rewrite the equation as $- \frac{1}{0.0075} \cdot \ln (\frac{0.00004 - 0.5}{a (0.5)}) = t$ .

$- \frac{1}{0.0075} \cdot \ln (\frac{0.00004 - 0.5}{a (0.5)}) = t$

Step 2

Simplify $- \frac{1}{0.0075} \cdot \ln (\frac{0.00004 - 0.5}{a (0.5)})$ .

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Step 2.1

Simplify the expression.

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Step 2.1.1

Divide $1$ by $0.0075$ .

$- 1 \cdot 133.\overline{3} \cdot \ln (\frac{0.00004 - 0.5}{a (0.5)}) = t$

Step 2.1.2

Multiply $- 1$ by $133.\overline{3}$ .

$- 133.\overline{3} \cdot \ln (\frac{0.00004 - 0.5}{a (0.5)}) = t$

Step 2.1.3

Subtract $0.5$ from $0.00004$ .

$- 133.\overline{3} \cdot \ln (\frac{- 0.49996}{a (0.5)}) = t$

Step 2.1.4

Move $0.5$ to the left of $a$ .

$- 133.\overline{3} \cdot \ln (\frac{- 0.49996}{0.5 a}) = t$

Step 2.1.5

Move the negative in front of the fraction.

$- 133.\overline{3} \cdot \ln (- \frac{0.49996}{0.5 a}) = t$

Step 2.2

Factor $0.49996$ out of $0.49996$ .

$- 133.\overline{3} \cdot \ln (- \frac{0.49996 (1)}{0.5 a}) = t$

Step 2.3

Factor $0.5$ out of $0.5 a$ .

$- 133.\overline{3} \cdot \ln (- \frac{0.49996 (1)}{0.5 (a)}) = t$

Step 2.4

Separate fractions.

$- 133.\overline{3} \cdot \ln (- (\frac{0.49996}{0.5} \cdot \frac{1}{a})) = t$

Step 2.5

Divide $0.49996$ by $0.5$ .

$- 133.\overline{3} \cdot \ln (- (0.99992 \frac{1}{a})) = t$

Step 2.6

Combine $0.99992$ and $\frac{1}{a}$ .

$- 133.\overline{3} \cdot \ln (- \frac{0.99992}{a}) = t$

Step 2.7

Simplify $- 133.\overline{3} \ln (- \frac{0.99992}{a})$ by moving $133.\overline{3}$ inside the logarithm.

$- \ln ({(- \frac{0.99992}{a})}^{133.\overline{3}}) = t$

Step 2.8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.8.1

Apply the product rule to $- \frac{0.99992}{a}$ .

$- \ln ({(- 1)}^{133.\overline{3}} {(\frac{0.99992}{a})}^{133.\overline{3}}) = t$

Step 2.8.2

Apply the product rule to $\frac{0.99992}{a}$ .

$- \ln ({(- 1)}^{133.\overline{3}} \frac{{0.99992}^{133.\overline{3}}}{a^{133.\overline{3}}}) = t$

Step 2.9

Raise $0.99992$ to the power of $133.\overline{3}$ .

$- \ln ({(- 1)}^{133.\overline{3}} \frac{0.98938959}{a^{133.\overline{3}}}) = t$

Step 2.10

Combine ${(- 1)}^{133.\overline{3}}$ and $\frac{0.98938959}{a^{133.\overline{3}}}$ .

$- \ln (\frac{{(- 1)}^{133.\overline{3}} \cdot 0.98938959}{a^{133.\overline{3}}}) = t$

Step 2.11

Move $0.98938959$ to the left of ${(- 1)}^{133.\overline{3}}$ .

$- \ln (\frac{0.98938959 {(- 1)}^{133.\overline{3}}}{a^{133.\overline{3}}}) = t$