Precalculus Examples

$\frac{\ln (\frac{363}{282})}{\ln (1.01)} + 1995$

Step 1

Cancel the common factor of $363$ and $282$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $363$ .

$\frac{\ln (\frac{3 (121)}{282})}{\ln (1.01)} + 1995$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $3$ out of $282$ .

$\frac{\ln (\frac{3 \cdot 121}{3 \cdot 94})}{\ln (1.01)} + 1995$

Step 1.2.2

Cancel the common factor.

$\frac{\ln (\frac{3 \cdot 121}{3 \cdot 94})}{\ln (1.01)} + 1995$

Step 1.2.3

Rewrite the expression.

$\frac{\ln (\frac{121}{94})}{\ln (1.01)} + 1995$

Step 2

To write $1995$ as a fraction with a common denominator, multiply by $\frac{\ln (1.01)}{\ln (1.01)}$ .

$\frac{\ln (\frac{121}{94})}{\ln (1.01)} + \frac{1995 \ln (1.01)}{\ln (1.01)}$

Step 3

Combine the numerators over the common denominator.

$\frac{\ln (\frac{121}{94}) + 1995 \ln (1.01)}{\ln (1.01)}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Simplify $1995 \ln (1.01)$ by moving $1995$ inside the logarithm.

$\frac{\ln (\frac{121}{94}) + \ln ({1.01}^{1995})}{\ln (1.01)}$

Step 4.2

Raise $1.01$ to the power of $1995$ .

$\frac{\ln (\frac{121}{94}) + \ln (417965751.144156)}{\ln (1.01)}$

Step 4.3

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

$\frac{\ln (\frac{121}{94} \cdot 417965751.144156)}{\ln (1.01)}$

Step 4.4

Multiply $\frac{121}{94} \cdot 417965751.144156$ .

Tap for more steps...

Step 4.4.1

Combine $\frac{121}{94}$ and $417965751.144156$ .

$\frac{\ln (\frac{121 \cdot 417965751.144156}{94})}{\ln (1.01)}$

Step 4.4.2

Multiply $121$ by $417965751.144156$ .

$\frac{\ln (\frac{50573855888.442876}{94})}{\ln (1.01)}$

Step 4.5

Divide $50573855888.442876$ by $94$ .

$\frac{\ln (538019743.49407314)}{\ln (1.01)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (538019743.49407314)}{\ln (1.01)}$

Decimal Form:

$2020.37561484 \dots$