Precalculus Examples

$500 e^{0.6 x} = 850$

Step 1

Simplify.

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Step 1.1

Divide each term in $500 e^{0.6 x} = 850$ by $500$ .

$\frac{500 e^{0.6 x}}{500} = \frac{850}{500}$

Step 1.2

Cancel the common factor of $850$ and $500$ .

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Step 1.2.1

Factor $50$ out of $850$ .

$\frac{50 (17)}{500}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $50$ out of $500$ .

$\frac{50 \cdot 17}{50 \cdot 10}$

Step 1.2.2.2

Cancel the common factor.

$\frac{50 \cdot 17}{50 \cdot 10}$

Step 1.2.2.3

Rewrite the expression.

$\frac{17}{10}$

Step 1.3

Reduce by cancelling the common factors.

$e^{0.6 x} = \frac{17}{10}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the right side $(\frac{17}{10})$ equals the exponent $(0.6 x)$ .

$\log_{e} (\frac{17}{10}) = 0.6 x$