What is the solution for e^(2x+1)=8?

Question

Thank you show work please

Answer 1

e^(2x+1)=8

take the ln of both sides and use the fact that
ln(a^m) = m ln(a)

2x +1 = ln(8)
2x = -1 +ln(8)
x = -1/2 + ln(8)/2

x = 0.5397

Answer 2

We are using logs to solve exponential equations.

We have this:

e^(2x + 1) = 8

We can get an exact solution by changing the exponential equation to logs.

In8 = 2x + 1

By the way, "In" means THE NATURAL LOG.

We subtract 1 from the natural log of 8 using our calculator.

In8 - 1 = 2x

1.079441542 = 2x

Divide both sides by 2 to find the value of x.

1.079441542 divided by 2 = x

0.539720771 is approximately x, which can be rounded off to the nearest thousandths.

x is approximately 0.540.

However, if you rounded off to the nearest ten thousandths, the answer is: x is approximately 0.5397

Answer 3

Hello,

Take the ln of both sides giving us ln e^(2x+1) = ln 8

so (2x+1) ln e = ln 8 but ln e = 1 so we have 2x+1 = ln8 then
2x = ln 8 -1 or x = (ln 8 -1)/2 then x = (2.0794 -1)/2 = 0.5397

Checking we have e^(2*0.5397 +1)) should be 8

e^(2*.8664) = e^(1.6932) = 8

It Checks.

Hope This Helps!!