2e^3x=16

Solve for x.

So far I changed this to 2ln3x=16 then ln3x=8 then...

e^3x=8

ln each side
3x=ln(8)=2.08

Thank you

To solve for x in the equation 2e^(3x) = 16, let's continue from where you left off.

You correctly changed the equation to 2ln(3x) = 16. Now, to isolate ln(3x), divide both sides of the equation by 2:

2ln(3x)/2 = 16/2

ln(3x) = 8

Next, we need to eliminate the natural logarithm by exponentiating both sides of the equation with e (the base of the natural logarithm):

e^(ln(3x)) = e^8

By the property of logarithms, the exponential cancels out the logarithm:

3x = e^8

Now, to solve for x, divide both sides of the equation by 3:

3x/3 = e^8/3

x = e^8/3

Therefore, the solution for x is x = e^8/3.

To solve the equation 2e^(3x) = 16 for x, you have correctly started by taking the natural logarithm (ln) of both sides to eliminate the exponential term.

You obtained 2ln(3x) = 16.

To continue, you need to isolate the logarithmic term. Divide both sides of the equation by 2:

ln(3x) = 8 / 2

This simplifies to:

ln(3x) = 4

Next, you can use the exponential property of logarithms to eliminate the natural logarithm. The exponential form of the logarithmic equation ln(3x) = 4 is e^4 = 3x.

Now, divide both sides of the equation by 3 to isolate x:

e^4 / 3 = 3x / 3

Simplifying further:

x = e^4 / 3

Therefore, the solution to the equation 2e^(3x) = 16 is x = e^4 / 3.