Precalculus Examples

$\frac{\ln (\frac{323}{283})}{\ln (1.011)} + 1997$

Step 1

To write $1997$ as a fraction with a common denominator, multiply by $\frac{\ln (1.011)}{\ln (1.011)}$ .

$\frac{\ln (\frac{323}{283})}{\ln (1.011)} + \frac{1997 \ln (1.011)}{\ln (1.011)}$

Step 2

Combine the numerators over the common denominator.

$\frac{\ln (\frac{323}{283}) + 1997 \ln (1.011)}{\ln (1.011)}$

Step 3

Simplify the numerator.

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Step 3.1

Simplify $1997 \ln (1.011)$ by moving $1997$ inside the logarithm.

$\frac{\ln (\frac{323}{283}) + \ln ({1.011}^{1997})}{\ln (1.011)}$

Step 3.2

Raise $1.011$ to the power of $1997$ .

$\frac{\ln (\frac{323}{283}) + \ln (3076505637.41055)}{\ln (1.011)}$

Step 3.3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\ln (\frac{323}{283} \cdot 3076505637.41055)}{\ln (1.011)}$

Step 3.4

Multiply $\frac{323}{283} \cdot 3076505637.41055$ .

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Step 3.4.1

Combine $\frac{323}{283}$ and $3076505637.41055$ .

$\frac{\ln (\frac{323 \cdot 3076505637.41055}{283})}{\ln (1.011)}$

Step 3.4.2

Multiply $323$ by $3076505637.41055$ .

$\frac{\ln (\frac{993711320883.60765}{283})}{\ln (1.011)}$

Step 3.5

Divide $993711320883.60765$ by $283$ .

$\frac{\ln (3511347423.61698816)}{\ln (1.011)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (3511347423.61698816)}{\ln (1.011)}$

Decimal Form:

$2009.08465723 \dots$