solve for the unknown:
6e^(-4t) = 2
6*e^(-4t) = 2
e^(-4t) = 1/3
take the ln of both sides:
ln [ e^(-4t) ] = ln (1/3)
-4t = ln (1/3)
t = -(1/4)*(ln (1/3)) or
t = (1/4)*(ln 3)
hope this helps~ :)
Well, solving for the unknown is a serious business, but I'll do my best to keep it light-hearted!
To solve this equation, we need to isolate the variable "t." It's like trying to separate a pair of socks that are stuck together - challenging but not impossible!
First, let's divide both sides of the equation by 6 to simplify things:
e^(-4t) = 2/6
Now, we can take the natural logarithm (ln) of both sides to get rid of the exponential:
ln(e^(-4t)) = ln(2/6)
Ah, lo and behold, the natural logarithm! It's like a magical wand that can make exponential functions disappear.
Now, using the property of logarithms, we can bring down the power of -4t:
-4t * ln(e) = ln(2/6)
But hold on a second, the natural logarithm of e is just 1! So, we're left with:
-4t = ln(2/6)
Or should I say, "negative 4t caught the sneaky serpent of the natural logarithm"?
To find "t," we can go ahead and divide both sides by -4:
t = ln(2/6) / -4
And ta-da! We have cracked the code and found our answer. Just make sure to grab your calculator to calculate the value of ln(2/6) and divide it by -4!
Remember, always approach math problems with a smile—anything is possible with a little humor!
To solve for the unknown variable, we need to isolate it on one side of the equation.
Step 1: Divide both sides of the equation by 6.
(6e^(-4t))/6 = 2/6
This simplifies to:
e^(-4t) = 1/3
Step 2: Take the natural logarithm (ln) of both sides of the equation to eliminate the exponent.
ln(e^(-4t)) = ln(1/3)
By using the property of logarithms, we can bring down the exponent:
-4t * ln(e) = ln(1/3)
Since the natural logarithm of e is equal to 1, we have:
-4t = ln(1/3)
Step 3: Divide both sides of the equation by -4 to solve for t:
(-4t)/-4 = ln(1/3)/-4
This simplifies to:
t = -ln(1/3)/4
or
t = (ln(3)-ln(1))/4
Thus, the solution for the unknown variable is t = (ln(3)-ln(1))/4.
To solve for the unknown variable, we can follow these steps:
Step 1: Divide both sides of the equation by 6 to isolate the exponential term:
(6e^(-4t)) / 6 = 2 / 6
Simplifying this step, we get:
e^(-4t) = 1/3
Step 2: Take the natural logarithm (ln) of both sides of the equation to remove the exponential term:
ln(e^(-4t)) = ln(1/3)
Using the property of logarithms, ln(e^x) = x, we have:
-4t = ln(1/3)
Step 3: Divide both sides of the equation by -4 to solve for "t":
(-4t) / -4 = ln(1/3) / -4
Simplifying this step, we get:
t = ln(1/3) / 4
Therefore, the value of the unknown variable "t" is given by the expression ln(1/3) divided by 4.