Precalculus Examples

$- 2 + \frac{\ln (339)}{\ln (2)}$

Step 1

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{\ln (2)}{\ln (2)}$ .

$- 2 \cdot \frac{\ln (2)}{\ln (2)} + \frac{\ln (339)}{\ln (2)}$

Step 2

Combine fractions.

Tap for more steps...

Step 2.1

Combine $- 2$ and $\frac{\ln (2)}{\ln (2)}$ .

$\frac{- 2 \ln (2)}{\ln (2)} + \frac{\ln (339)}{\ln (2)}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{- 2 \ln (2) + \ln (339)}{\ln (2)}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Simplify $- 2 \ln (2)$ by moving $2$ inside the logarithm.

$\frac{- \ln (2^{2}) + \ln (339)}{\ln (2)}$

Step 3.2

Raise $2$ to the power of $2$ .

$\frac{- \ln (4) + \ln (339)}{\ln (2)}$

Step 4

Simplify with factoring out.

Tap for more steps...

Step 4.1

Factor $- 1$ out of $- \ln (4)$ .

$\frac{- (\ln (4)) + \ln (339)}{\ln (2)}$

Step 4.2

Factor $- 1$ out of $\ln (339)$ .

$\frac{- (\ln (4)) - 1 (- \ln (339))}{\ln (2)}$

Step 4.3

Factor $- 1$ out of $- (\ln (4)) - 1 (- \ln (339))$ .

$\frac{- (\ln (4) - \ln (339))}{\ln (2)}$

Step 4.4

Simplify the expression.

Tap for more steps...

Step 4.4.1

Rewrite $- (\ln (4) - \ln (339))$ as $- 1 (\ln (4) - \ln (339))$ .

$\frac{- 1 (\ln (4) - \ln (339))}{\ln (2)}$

Step 4.4.2

Move the negative in front of the fraction.

$- \frac{\ln (4) - \ln (339)}{\ln (2)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\ln (4) - \ln (339)}{\ln (2)}$

Decimal Form:

$6.40514146 \dots$