Precálculo Ejemplos

$- \frac{\ln (A) - \ln (1500)}{64.3775165 + 20 \ln (n) - 20 \ln (25 n + 3)}$

Paso 1

Usa la propiedad del cociente de los logaritmos, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$- \frac{\ln (\frac{A}{1500})}{64.3775165 + 20 \ln (n) - 20 \ln (25 n + 3)}$

Paso 2

Simplifica el denominador.

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Paso 2.1

Factoriza $0.0000005$ de $64.3775165 + 20 \ln (n) - 20 \ln (25 n + 3)$ .

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Paso 2.1.1

Factoriza $0.0000005$ de $64.3775165$ .

$- \frac{\ln (\frac{A}{1500})}{0.0000005 (128755033) + 20 \ln (n) - 20 \ln (25 n + 3)}$

Paso 2.1.2

Factoriza $0.0000005$ de $20 \ln (n)$ .

$- \frac{\ln (\frac{A}{1500})}{0.0000005 (128755033) + 0.0000005 (40000000 \ln (n)) - 20 \ln (25 n + 3)}$

Paso 2.1.3

Factoriza $0.0000005$ de $- 20 \ln (25 n + 3)$ .

$- \frac{\ln (\frac{A}{1500})}{0.0000005 (128755033) + 0.0000005 (40000000 \ln (n)) + 0.0000005 (- 40000000 \ln (25 n + 3))}$

Paso 2.1.4

Factoriza $0.0000005$ de $0.0000005 (128755033) + 0.0000005 (40000000 \ln (n))$ .

$- \frac{\ln (\frac{A}{1500})}{0.0000005 (128755033 + 40000000 \ln (n)) + 0.0000005 (- 40000000 \ln (25 n + 3))}$

Paso 2.1.5

Factoriza $0.0000005$ de $0.0000005 (128755033 + 40000000 \ln (n)) + 0.0000005 (- 40000000 \ln (25 n + 3))$ .

$- \frac{\ln (\frac{A}{1500})}{0.0000005 (128755033 + 40000000 \ln (n) - 40000000 \ln (25 n + 3))}$

Paso 2.2

Simplifica $40000000 \ln (n)$ al mover $40000000$ dentro del algoritmo.

$- \frac{\ln (\frac{A}{1500})}{0.0000005 (128755033 + \ln (n^{40000000}) - 40000000 \ln (25 n + 3))}$

Paso 2.3

Simplifica $- 40000000 \ln (25 n + 3)$ al mover $40000000$ dentro del algoritmo.

$- \frac{\ln (\frac{A}{1500})}{0.0000005 (128755033 + \ln (n^{40000000}) - \ln ({(25 n + 3)}^{40000000}))}$

Paso 2.4

Usa la propiedad del cociente de los logaritmos, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$- \frac{\ln (\frac{A}{1500})}{0.0000005 (128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}}))}$

Paso 3

Multiplica por $1$ .

$- \frac{1 \ln (\frac{A}{1500})}{0.0000005 (128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}}))}$

Paso 4

Separa las fracciones.

$- (\frac{1}{0.0000005} \cdot \frac{\ln (\frac{A}{1500})}{128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}})})$

Paso 5

Divide $1$ por $0.0000005$ .

$- (2000000 \frac{\ln (\frac{A}{1500})}{128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}})})$

Paso 6

Multiplica $2000000 \frac{\ln (\frac{A}{1500})}{128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}})}$ .

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Paso 6.1

Combina $2000000$ y $\frac{\ln (\frac{A}{1500})}{128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}})}$ .

$- \frac{2000000 \ln (\frac{A}{1500})}{128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}})}$

Paso 6.2

Simplifica $2000000 \ln (\frac{A}{1500})$ al mover $2000000$ dentro del algoritmo.

$- \frac{\ln ({(\frac{A}{1500})}^{2000000})}{128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}})}$

Paso 7

Aplica la regla del producto a $\frac{A}{1500}$ .

$- \frac{\ln (\frac{A^{2000000}}{1500^{2000000}})}{128755033 + \ln (\frac{n^{40000000}}{{(25 n + 3)}^{40000000}})}$