Question

Solve the equation
ln(x^6 )−ln(x ^2 )=ln(2x^4 ).

Answer 1

To solve the equation ln(x^6 )−ln(x^2 )=ln(2x^4 ), use properties of logarithms to simplify the equation and find the solution.

Step-by-step explanation:

To solve the equation ln(x^6)−ln(x^2)=ln(2x^4), we can use the properties of logarithms.

First, using the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers, we can simplify the equation to ln(x^6 / x^2) = ln(2x^4).

Next, using the property that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, we can further simplify the equation to ln(x^4) = ln(2x^4).

Finally, using the property that the natural logarithm of a number (In) is the power to which e must be raised to equal the number, we can conclude that x^4 = 2x^4, which leads to the solution x = 1/√2.