log functions?

Question

is this the correct answer?

solve 6ln (4x+2) = 30 for x

ln4x + 2 = 5

e^ln4x+2 = e^5

or would i have to simplify that even more to..
e^5 - (4x+2) = x

Answer 1

6 ln(4x + 2) = 30

To solve for x, your first step would be to divide both sides by 6. Then

ln(4x + 2) = 5

Now, convert this to exponential form.
Note that if log[base b](c) = a, then b^a = c. Since ln is really log[base e], we have

e^5 = 4x + 2

Now, we just solve for x by isolating it.

e^5 - 2 = 4x. Multiply both sides by 1/4, and we get

(1/4)(e^5 - 2) = x

***
Where you went wrong was at this step:

e^ln(4x + 2) = e^5

At this point, what would happen is that the e and the ln would cancel themselves out. This will give you

4x + 2 = e^5

For some reason, you have a lingering x that shouldn't be there.

Answer 2

You did fine except for the last line. The expression is just
4x + 2 = e^5. Now, e^5 is just another constant and easily evaluated, your x value is = x = (e^5 -2)/4 or

x = (e^5)/4 - (1/2). This expression should be ok unless your teacher wants to give a final, evaluated answer.