Reiny
answered
ln4 + ln(3x) = 4
then
ln(12x) = 4
12x = e^4
x = e^4/12 , you do the button pushing.
Damon
answered
if so
ln (4*3x) = 2
ln (12 x ) = 2
e^ln12x = 12 x = e^2
x = e^2/12
Reiny
answered
Clown Bot
answered
Let's tackle the equation given to us: 4 + ln(3x) = 2.
To solve this equation, we need to isolate the natural logarithm term. So, we'll start by subtracting 4 from both sides:
ln(3x) = 2 - 4
Now, let's simplify the right side:
ln(3x) = -2
To get rid of the natural logarithm, we'll exponentiate both sides using e (that fancy number that makes clown noses pop):
e^(ln(3x)) = e^(-2)
By the magical property of logarithms and exponential functions canceling each other out, we're left with:
3x = e^(-2)
Now, divide both sides by 3:
x = (e^(-2))/3
Now, if we want to round this lovely solution to the nearest hundredth (because decimals are friends too), we'll need to whip out our trusty calculator or computer program:
x ≈ 0.049787068
So, my dear friend, the solution to the equation 4 + ln(3x) = 2, rounded to the nearest hundredth, is approximately x = 0.05. Ta-da!
Explain Bot
answered
Step 1: Subtract 4 from both sides of the equation:
4 + ln(3x) - 4 = 2 - 4
This simplifies to:
ln(3x) = -2
Step 2: Rewrite the equation using exponentiation:
e^(ln(3x)) = e^(-2)
Step 3: Simplify the left side using the inverse property of logarithms:
3x = e^(-2)
Step 4: Divide both sides of the equation by 3:
3x / 3 = e^(-2) / 3
Simplifying further:
x = e^(-2) / 3
Now, you can calculate the approximate value of x by evaluating e^(-2) and dividing it by 3.
Using a calculator, e^(-2) is approximately 0.135335.
Dividing 0.135335 by 3 gives an approximate value of x:
x ≈ 0.045
Rounding to the nearest hundredth, the solution to the equation is x ≈ 0.05.
