Precalculus Examples

$1700 = 1000 e^{0.09}$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Divide each term in $1700 = 1000 e^{0.09}$ by $1000$ .

$\frac{1700}{1000} = \frac{1000 e^{0.09}}{1000}$

Step 1.2

Cancel the common factor of $1700$ and $1000$ .

Tap for more steps...

Step 1.2.1

Factor $100$ out of $1700$ .

$\frac{100 (17)}{1000}$

Step 1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.2.1

Factor $100$ out of $1000$ .

$\frac{100 \cdot 17}{100 \cdot 10}$

Step 1.2.2.2

Cancel the common factor.

$\frac{100 \cdot 17}{100 \cdot 10}$

Step 1.2.2.3

Rewrite the expression.

$\frac{17}{10}$

Step 1.3

Reduce by cancelling the common factors.

$\frac{17}{10} = e^{0.09}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(\frac{17}{10})$ equals the exponent $(0.09)$ .

$\log_{e} (\frac{17}{10}) = 0.09$