Precalculus Examples

$20 = 50 {(1.04)}^{x}$

Step 1

Simplify.

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Step 1.1

Remove parentheses.

$20 = 50 \cdot {1.04}^{x}$

Step 1.2

Divide each term in $20 = 50 \cdot {1.04}^{x}$ by $50$ .

$\frac{20}{50} = \frac{50 \cdot {1.04}^{x}}{50}$

Step 1.3

Cancel the common factor of $20$ and $50$ .

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Step 1.3.1

Factor $10$ out of $20$ .

$\frac{10 (2)}{50}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $10$ out of $50$ .

$\frac{10 \cdot 2}{10 \cdot 5}$

Step 1.3.2.2

Cancel the common factor.

$\frac{10 \cdot 2}{10 \cdot 5}$

Step 1.3.2.3

Rewrite the expression.

$\frac{2}{5}$

Step 1.4

Reduce by cancelling the common factors.

$\frac{2}{5} = {1.04}^{x}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(1.04)$ of the left side $(\frac{2}{5})$ equals the exponent $(x)$ .

$\log_{1.04} (\frac{2}{5}) = x$