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.