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Solve the logarithmic equation $1000\left(x+1\right)x^{\log_{x}\left(x+1\right)}=\left(x+1\right)^{\log \left(x+1\right)}$

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Solution

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Step-by-step Solution

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  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
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Simplifying the logarithm

Learn how to solve logarithmic equations problems step by step online.

$1000\left(x+1\right)\cdot \left(x+1\right)=\left(x+1\right)^{\log \left(x+1\right)}$

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Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation 1000(x+1)x^logx(x+1)=(x+1)^log(x+1). Simplifying the logarithm. When multiplying two powers that have the same base (x+1), you can add the exponents. Expand the expression \left(x+1\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Grouping all terms to the left side of the equation.

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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$2\cdot log\left(x\right)-1\cdot log\left(x+6\right)=0$

Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

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