How can i find the ln of both sides of the equation?
6=6e^3x
and O.2= e^-kt
ln 6 = ln6 + 3x
which means x = 0
ln 0.2 = -1.609 = -kt
which means kt = 1.609
To find the natural logarithm of both sides of an equation, you can follow these steps:
Step 1: Start with the equation you're given:
6 = 6e^(3x)
Step 2: Take the natural logarithm (ln) of both sides of the equation. Remember that ln is the inverse function of e^x, so taking logarithm of both sides will isolate the exponent:
ln(6) = ln(6e^(3x))
Step 3: Use the properties of logarithms to simplify the equation. Specifically, you can use the rule ln(a * b) = ln(a) + ln(b):
ln(6) = ln(6) + ln(e^(3x))
Step 4: Since ln(e^x) = x, you can simplify further:
ln(6) = ln(6) + 3x
Now, let's move on to the second equation:
Given equation: 0.2 = e^(-kt)
To find the natural logarithm of both sides, follow these steps:
Step 1: Start with the equation you're given:
0.2 = e^(-kt)
Step 2: Take the natural logarithm (ln) of both sides of the equation:
ln(0.2) = ln(e^(-kt))
Step 3: Simplify using the property of logarithms:
ln(0.2) = -kt
These steps show you how to find the ln of both sides of the equations and simplify them.