Precalculus Examples

$18000 = 8000 {(b)}^{30}$

Step 1

Simplify.

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Step 1.1

Remove parentheses.

$18000 = 8000 b^{30}$

Step 1.2

Divide each term in $18000 = 8000 b^{30}$ by $8000$ .

$\frac{18000}{8000} = \frac{8000 b^{30}}{8000}$

Step 1.3

Cancel the common factor of $18000$ and $8000$ .

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Step 1.3.1

Factor $2000$ out of $18000$ .

$\frac{2000 (9)}{8000}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2000$ out of $8000$ .

$\frac{2000 \cdot 9}{2000 \cdot 4}$

Step 1.3.2.2

Cancel the common factor.

$\frac{2000 \cdot 9}{2000 \cdot 4}$

Step 1.3.2.3

Rewrite the expression.

$\frac{9}{4}$

Step 1.4

Reduce by cancelling the common factors.

$\frac{9}{4} = b^{30}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(b)$ of the left side $(\frac{9}{4})$ equals the exponent $(30)$ .

$\log_{b} (\frac{9}{4}) = 30$