Basic Math Examples

$(\frac{t}{5600}) \log (0.5) = \log (0.12)$

Step 1

Simplify the left side.

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Step 1.1

Combine $\frac{t}{5600}$ and $\log (0.5)$ .

$\frac{t \log (0.5)}{5600} = \log (0.12)$

Step 2

Move all the terms containing a logarithm to the left side of the equation.

$\frac{t \log (0.5)}{5600} - \log (0.12) = 0$

Step 3

Simplify each term.

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Step 3.1

Log base $10$ of $0.5$ is approximately $- 0.30102999$ .

$\frac{t \cdot - 0.30102999}{5600} - \log (0.12) = 0$

Step 3.2

Move $- 0.30102999$ to the left of $t$ .

$\frac{- 0.30102999 \cdot t}{5600} - \log (0.12) = 0$

Step 3.3

Move the negative in front of the fraction.

$- \frac{0.30102999 \cdot t}{5600} - \log (0.12) = 0$

Step 3.4

Factor $0.30102999$ out of $0.30102999 \cdot t$ .

$- \frac{0.30102999 (t)}{5600} - \log (0.12) = 0$

Step 3.5

Factor $5600$ out of $5600$ .

$- \frac{0.30102999 (t)}{5600 (1)} - \log (0.12) = 0$

Step 3.6

Separate fractions.

$- (\frac{0.30102999}{5600} \cdot \frac{t}{1}) - \log (0.12) = 0$

Step 3.7

Divide $0.30102999$ by $5600$ .

$- (0.00005375 (\frac{t}{1})) - \log (0.12) = 0$

Step 3.8

Divide $t$ by $1$ .

$- (0.00005375 t) - \log (0.12) = 0$

Step 3.9

Multiply $0.00005375$ by $- 1$ .

$- 0.00005375 t - \log (0.12) = 0$

Step 3.10

Log base $10$ of $0.12$ is approximately $- 0.92081875$ .

$- 0.00005375 t + 0.92081875 = 0$

Step 3.11

Multiply $- 1$ by $- 0.92081875$ .

$- 0.00005375 t + 0.92081875 = 0$

Step 4

Subtract $0.92081875$ from both sides of the equation.

$- 0.00005375 t = - 0.92081875$

Step 5

Divide each term in $- 0.00005375 t = - 0.92081875$ by $- 0.00005375$ and simplify.

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Step 5.1

Divide each term in $- 0.00005375 t = - 0.92081875$ by $- 0.00005375$ .

$\frac{- 0.00005375 t}{- 0.00005375} = \frac{- 0.92081875}{- 0.00005375}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 0.00005375$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 0.00005375 t}{- 0.00005375} = \frac{- 0.92081875}{- 0.00005375}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 0.92081875}{- 0.00005375}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 0.92081875$ by $- 0.00005375$ .

$t = 17129.80465869$