Precalculus Examples

$0.5 \cdot 10^{8 t} = 73$

Step 1

Divide each term in $0.5 \cdot 10^{8 t} = 73$ by $0.5$ and simplify.

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Step 1.1

Divide each term in $0.5 \cdot 10^{8 t} = 73$ by $0.5$ .

$\frac{0.5 \cdot 10^{8 t}}{0.5} = \frac{73}{0.5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $0.5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{0.5 \cdot 10^{8 t}}{0.5} = \frac{73}{0.5}$

Step 1.2.1.2

Divide $10^{8 t}$ by $1$ .

$10^{8 t} = \frac{73}{0.5}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $73$ by $0.5$ .

$10^{8 t} = 146$

Step 2

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

$\log (10^{8 t}) = \log (146)$

Step 3

Expand the left side.

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Step 3.1

Expand $\log (10^{8 t})$ by moving $8 t$ outside the logarithm.

$8 t \log (10) = \log (146)$

Step 3.2

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

$8 t \cdot 1 = \log (146)$

Step 3.3

Multiply $8$ by $1$ .

$8 t = \log (146)$

Step 4

Divide each term in $8 t = \log (146)$ by $8$ and simplify.

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Step 4.1

Divide each term in $8 t = \log (146)$ by $8$ .

$\frac{8 t}{8} = \frac{\log (146)}{8}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{8 t}{8} = \frac{\log (146)}{8}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{\log (146)}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\log (146)}{8}$

Decimal Form:

$t = 0.27054410 \dots$