I need help solving for this final problem to complete my assigment. Please help!

Solve for x:

ln(x^4)-ln(x^2)=2

I need help solving for this final problem to complete my assigment. Please help!

Solve for x:

ln(x^4)-ln(x^2)=2

Use your rules of logs

ln(x^4)-ln(x^2)=2
ln (x^4/x^2) = 2
ln(x^2) = 2
2 lnx = 2
lnx = 1
e^1 = x

x = e

or

ln(x^4)-ln(x^2)=2
4lnx - 2lnx = 2
2lnx = 2
lnx = 1
x = e^1 = e

thanks alot man, wow it makes alot of sense.

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

First, we can apply the quotient rule of logarithms, which states that ln(a) - ln(b) = ln(a / b). Applying this to the equation gives:

ln(x^4 / x^2) = 2.

Simplifying the expression inside the logarithm gives:

ln(x^2) = 2.

Now, we can rewrite this equation as an exponential equation, since logarithmic and exponential functions are inverses of each other.

Remember that ln(x) = y is equivalent to e^y = x. In this case, ln(x^2) = 2 is equivalent to e^2 = x^2.

Taking the square root of both sides gives:

sqrt(e^2) = sqrt(x^2).

Simplifying further, we have:

e = x.

Therefore, x = e.

So the solution to the equation ln(x^4) - ln(x^2) = 2 is x = e.