ln(2x-5)= 4
how do i this problem? thanks!
ln(2x-5) = 4
we raise both sides by e:
e^(ln(2x-5)) = e^4
the e and ln will be cancelled, leaving only the 2x - 5:
2x - 5 = e^4
2x = e^4 + 5
x = (e^4 + 5)/2
hope this helps~ :)
To solve this problem, you can follow these steps:
Step 1: Isolate the logarithmic expression.
In this case, you want to isolate the ln(2x-5) term. To do so, you can rewrite the equation as:
ln(2x-5) = 4
Step 2: Exponentiate both sides of the equation.
To eliminate the logarithm, you can exponentiate both sides of the equation using the exponential function e:
e^(ln(2x-5)) = e^4
Step 3: Simplify the left side.
Since e^(ln(x)) is the inverse function of ln(x), the left side simplifies to just (2x-5):
2x-5 = e^4
Step 4: Solve for x.
Now you can solve the equation for x by isolating the variable.
Add 5 to both sides:
2x = e^4 + 5
Divide both sides by 2:
x = (e^4 + 5)/2
So, the solution to the equation ln(2x-5) = 4 is x = (e^4 + 5)/2.