Question

$1000(1 + 0.50) ^{n} = 5000$
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Answer 1

Respuesta:

$n=\frac{\ln \left(5\right)}{\ln \left(1.5\right)}$

Explicación paso a paso:

$1000\left(1+0.5\right)^n=5000$

$\mathrm{Dividir\:ambos\:lados\:entre\:}1000$

$\frac{1000\left(1+0.5\right)^n}{1000}=\frac{5000}{1000}$

$\mathrm{Simplificar}$

$\left(1+0.5\right)^n=5$

$\mathrm{Si\:}f\left(x\right)=g\left(x\right)\mathrm{,\:entonces\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)$

$\ln \left(\left(1+0.5\right)^n\right)=\ln \left(5\right)$

$\mathrm{Aplicar\:las\:propiedades\:de\:los\:logaritmos}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$n\ln \left(1+0.5\right)=\ln \left(5\right)$

$\mathrm{Resolver\:}\:n\ln \left(1+0.5\right)=\ln \left(5\right):\quad n=\frac{\ln \left(5\right)}{\ln \left(1.5\right)}$

$n=\frac{\ln \left(5\right)}{\ln \left(1.5\right)}$