Precalculus Examples

$p (114) = 1.7 {(1.0127)}^{t}$

Step 1

Simplify.

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Step 1.1

Remove parentheses.

$p (114) = 1.7 \cdot {1.0127}^{t}$

Step 1.2

Divide each term in $p (114) = 1.7 \cdot {1.0127}^{t}$ by $1.7$ .

$\frac{p (114)}{1.7} = \frac{1.7 \cdot {1.0127}^{t}}{1.7}$

Step 1.3

Move $114$ to the left of $p$ .

$\frac{114 p}{1.7}$

Step 1.4

Factor $114$ out of $114 p$ .

$\frac{114 (p)}{1.7}$

Step 1.5

Factor $1.7$ out of $1.7$ .

$\frac{114 (p)}{1.7 (1)}$

Step 1.6

Separate fractions.

$\frac{114}{1.7} \cdot \frac{p}{1}$

Step 1.7

Divide $114$ by $1.7$ .

$67.05882352 \frac{p}{1}$

Step 1.8

Divide $p$ by $1$ .

$67.05882352 p$

Step 1.9

Reduce by cancelling the common factors.

$67.05882352 p = {1.0127}^{t}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(1.0127)$ of the left side $(67.05882352 p)$ equals the exponent $(t)$ .

$\log_{1.0127} (67.05882352 p) = t$