Precalculus Examples

$1 = 17 {(0.99)}^{x}$

Step 1

Simplify.

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Step 1.1

Remove parentheses.

$1 = 17 \cdot {0.99}^{x}$

Step 1.2

Divide each term in $1 = 17 \cdot {0.99}^{x}$ by $17$ .

$\frac{1}{17} = \frac{17 \cdot {0.99}^{x}}{17}$

Step 1.3

Reduce by cancelling the common factors.

$\frac{1}{17} = {0.99}^{x}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(0.99)$ of the left side $(\frac{1}{17})$ equals the exponent $(x)$ .

$\log_{0.99} (\frac{1}{17}) = x$