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Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
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$\lim_{x\to\infty }\left(e^{\left(4x+3\right)\ln\left(\frac{2+5x}{1+5x}\right)}\right)$
Learn how to solve problems step by step online. Find the limit of ((2+5x)/(1+5x))^(4x+3) as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant. Rewrite the product inside the limit as a fraction.