Precalculus Examples

$\frac{\log (2)}{\log (1.0075)} = 12 x$

Step 1

Rewrite the equation as $12 x = \frac{\log (2)}{\log (1.0075)}$ .

$12 x = \frac{\log (2)}{\log (1.0075)}$

Step 2

Divide each term in $12 x = \frac{\log (2)}{\log (1.0075)}$ by $12$ and simplify.

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Step 2.1

Divide each term in $12 x = \frac{\log (2)}{\log (1.0075)}$ by $12$ .

$\frac{12 x}{12} = \frac{\frac{\log (2)}{\log (1.0075)}}{12}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{\frac{\log (2)}{\log (1.0075)}}{12}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{\log (2)}{\log (1.0075)}}{12}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{\log (2)}{\log (1.0075)} \cdot \frac{1}{12}$

Step 2.3.2

Multiply $\frac{\log (2)}{\log (1.0075)}$ by $\frac{1}{12}$ .

$x = \frac{\log (2)}{\log (1.0075) \cdot 12}$

Step 2.3.3

Move $12$ to the left of $\log (1.0075)$ .

$x = \frac{\log (2)}{12 \log (1.0075)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\log (2)}{12 \log (1.0075)}$

Decimal Form:

$x = 7.73048050 \dots$