Precalculus Examples

$y = 1.4 {(1.9)}^{x}$

Step 1

Simplify.

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Step 1.1

Remove parentheses.

$y = 1.4 \cdot {1.9}^{x}$

Step 1.2

Divide each term in $y = 1.4 \cdot {1.9}^{x}$ by $1.4$ .

$\frac{y}{1.4} = \frac{1.4 \cdot {1.9}^{x}}{1.4}$

Step 1.3

Multiply by $1$ .

$\frac{1 y}{1.4}$

Step 1.4

Factor $1.4$ out of $1.4$ .

$\frac{1 y}{1.4 (1)}$

Step 1.5

Separate fractions.

$\frac{1}{1.4} \cdot \frac{y}{1}$

Step 1.6

Divide $1$ by $1.4$ .

$0.\overline{714285} \frac{y}{1}$

Step 1.7

Divide $y$ by $1$ .

$0.\overline{714285} y$

Step 1.8

Reduce by cancelling the common factors.

$0.\overline{714285} y = {1.9}^{x}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(1.9)$ of the left side $(0.\overline{714285} y)$ equals the exponent $(x)$ .

$\log_{1.9} (0.\overline{714285} y) = x$