Precalculus Examples

$1500 {(1.2)}^{x} = 3000$

Step 1

Simplify.

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Step 1.1

Remove parentheses.

$1500 \cdot {1.2}^{x} = 3000$

Step 1.2

Divide each term in $1500 \cdot {1.2}^{x} = 3000$ by $1500$ .

$\frac{1500 \cdot {1.2}^{x}}{1500} = \frac{3000}{1500}$

Step 1.3

Divide $3000$ by $1500$ .

$2$

Step 1.4

Reduce by cancelling the common factors.

${1.2}^{x} = 2$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(1.2)$ of the right side $(2)$ equals the exponent $(x)$ .

$\log_{1.2} (2) = x$