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.