Find the Exact Value 1/( log base 2 of 12)+1/( log base 8 of 12)+1/( log base 9 of 12)

$\frac{1}{\log_{2} (12)} + \frac{1}{\log_{8} (12)} + \frac{1}{\log_{9} (12)}$

To write $\frac{1}{\log_{2} (12)}$ as a fraction with a common denominator, multiply by $\frac{\log_{8} (12)}{\log_{8} (12)}$ .

$\frac{1}{\log_{2} (12)} \cdot \frac{\log_{8} (12)}{\log_{8} (12)} + \frac{1}{\log_{8} (12)} + \frac{1}{\log_{9} (12)}$

To write $\frac{1}{\log_{8} (12)}$ as a fraction with a common denominator, multiply by $\frac{\log_{2} (12)}{\log_{2} (12)}$ .

$\frac{1}{\log_{2} (12)} \cdot \frac{\log_{8} (12)}{\log_{8} (12)} + \frac{1}{\log_{8} (12)} \cdot \frac{\log_{2} (12)}{\log_{2} (12)} + \frac{1}{\log_{9} (12)}$

Write each expression with a common denominator of $\log_{2} (12) \log_{8} (12)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{\log_{2} (12)}$ by $\frac{\log_{8} (12)}{\log_{8} (12)}$ .

$\frac{\log_{8} (12)}{\log_{2} (12) \log_{8} (12)} + \frac{1}{\log_{8} (12)} \cdot \frac{\log_{2} (12)}{\log_{2} (12)} + \frac{1}{\log_{9} (12)}$

Multiply $\frac{1}{\log_{8} (12)}$ by $\frac{\log_{2} (12)}{\log_{2} (12)}$ .

$\frac{\log_{8} (12)}{\log_{2} (12) \log_{8} (12)} + \frac{\log_{2} (12)}{\log_{8} (12) \log_{2} (12)} + \frac{1}{\log_{9} (12)}$

Reorder the factors of $\log_{8} (12) \log_{2} (12)$ .

$\frac{\log_{8} (12)}{\log_{2} (12) \log_{8} (12)} + \frac{\log_{2} (12)}{\log_{2} (12) \log_{8} (12)} + \frac{1}{\log_{9} (12)}$

Combine the numerators over the common denominator.

$\frac{\log_{8} (12) + \log_{2} (12)}{\log_{2} (12) \log_{8} (12)} + \frac{1}{\log_{9} (12)}$

To write $\frac{\log_{8} (12) + \log_{2} (12)}{\log_{2} (12) \log_{8} (12)}$ as a fraction with a common denominator, multiply by $\frac{\log_{9} (12)}{\log_{9} (12)}$ .

$\frac{\log_{8} (12) + \log_{2} (12)}{\log_{2} (12) \log_{8} (12)} \cdot \frac{\log_{9} (12)}{\log_{9} (12)} + \frac{1}{\log_{9} (12)}$

To write $\frac{1}{\log_{9} (12)}$ as a fraction with a common denominator, multiply by $\frac{\log_{2} (12) \log_{8} (12)}{\log_{2} (12) \log_{8} (12)}$ .

$\frac{\log_{8} (12) + \log_{2} (12)}{\log_{2} (12) \log_{8} (12)} \cdot \frac{\log_{9} (12)}{\log_{9} (12)} + \frac{1}{\log_{9} (12)} \cdot \frac{\log_{2} (12) \log_{8} (12)}{\log_{2} (12) \log_{8} (12)}$

Write each expression with a common denominator of $\log_{2} (12) \log_{8} (12) \log_{9} (12)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{\log_{8} (12) + \log_{2} (12)}{\log_{2} (12) \log_{8} (12)}$ by $\frac{\log_{9} (12)}{\log_{9} (12)}$ .

$\frac{(\log_{8} (12) + \log_{2} (12)) \log_{9} (12)}{\log_{2} (12) \log_{8} (12) \log_{9} (12)} + \frac{1}{\log_{9} (12)} \cdot \frac{\log_{2} (12) \log_{8} (12)}{\log_{2} (12) \log_{8} (12)}$

Multiply $\frac{1}{\log_{9} (12)}$ by $\frac{\log_{2} (12) \log_{8} (12)}{\log_{2} (12) \log_{8} (12)}$ .

$\frac{(\log_{8} (12) + \log_{2} (12)) \log_{9} (12)}{\log_{2} (12) \log_{8} (12) \log_{9} (12)} + \frac{\log_{2} (12) \log_{8} (12)}{\log_{9} (12) (\log_{2} (12) \log_{8} (12))}$

Reorder the factors of $\log_{9} (12) (\log_{2} (12) \log_{8} (12))$ .

$\frac{(\log_{8} (12) + \log_{2} (12)) \log_{9} (12)}{\log_{2} (12) \log_{8} (12) \log_{9} (12)} + \frac{\log_{2} (12) \log_{8} (12)}{\log_{2} (12) \log_{8} (12) \log_{9} (12)}$

Combine the numerators over the common denominator.

$\frac{(\log_{8} (12) + \log_{2} (12)) \log_{9} (12) + \log_{2} (12) \log_{8} (12)}{\log_{2} (12) \log_{8} (12) \log_{9} (12)}$

Apply the distributive property.

$\frac{\log_{8} (12) \log_{9} (12) + \log_{2} (12) \log_{9} (12) + \log_{2} (12) \log_{8} (12)}{\log_{2} (12) \log_{8} (12) \log_{9} (12)}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\log_{8} (12) \log_{9} (12) + \log_{2} (12) \log_{9} (12) + \log_{2} (12) \log_{8} (12)}{\log_{2} (12) \log_{8} (12) \log_{9} (12)}$

Decimal Form:

$2$

Find the Exact Value 1/( log base 2 of 12)+1/( log base 8 of 12)+1/( log base 9 of 12)

Related Questions

Support LCMGCF.com by disabling your adblocker.