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Solve 5xln2=(2x+1)ln3

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Final answer:

To solve the equation 5xln2 = (2x+1)ln3, properties of logarithms and exponents are used, along with the inverse relationship between natural logarithm and exponential functions.

Step-by-step explanation:

To solve the equation 5xln2 = (2x+1)ln3, we must use properties of logarithms and exponents. Specifically, the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This equation can be solved using the following steps:

  • Isolate the variable x on one side of the equation.
  • Divide both sides of the equation by the coefficient of x to find its value.
  • Check the solution by substituting x back into the original equation.

Additionally, remember that the natural logarithm and exponential functions are inverses of each other, which means that eln(x) = x and ln(ex) = x.

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