Solve: 5e^2x+7 = 15?

Question

I understand to set it to logarithmic form, which would then lead it to be ln5 (15) = 2x+7 (I think), but not sure what to do next.

Answer 1

I assume you mean:
5 * e^(2x + 7) = 15

Divide both sides by 5:
e^(2x + 7) = 3

Take the natural log (ln) of both sides:
2x + 7 = ln(3)

Subtract 7 from both sides:
2x = ln(3) - 7

Divide both sides by 2:
x = [ ln(3) - 7 ] / 2

For an approximate value, plug this in your calculator:
x ≈ -2.9507

Answer 2

Assuming the left side of the equation is
5e^2x+7 = 5e^(2x) + 7, we have the following...

Steps to solve:

1. Subtract 7 from both sides of the equation:
5e^2x = 8

2. Multiply both sides by 1/5:
e^2x = 8/5

3. Take the natural logarithm (ln) of both sides:
ln(e^2x) = ln(8/5)

4. Use the log rule ln(a^b) = b*ln(a) to manipulate ln(e^2x):
2x*ln(e) = ln(8/5)

5. Note that ln(e) is the solution w of the equation e^w = e ( = e^1), and thus ln(e) = 1:
2x * 1 = ln(8/5)

6. Solve for x:
x = (ln(8/5))/2

Depending on your or more probably your teacher's preference you can apply the log rule ln(a/b) = lna - lnb to get
x = (ln8 - ln5)/2,
but either is correct (they are the same number).

Answer 3

5e^2x+7 = 15 (divided both sides by 5)

e^2x + 7 = 3 (applied ''ln'' both sides)

(2x + 7) ln(e) = ln(3) (n.b.: ln(e) = 1)

2x + 7 = ln(3)

x = (ln(3) -7)/2

x = -2.9507

Answer 4

You need to put the parenthesis in the right place. is it e^(2x+7) or e^(2x) +7

:)