Question

Solve: e^2x + 5 = 4 help pls

Answer 1

Answer:

Answer is C on edge

Step-by-step explanation:

x= (ln 4)- 5/2

Answer 2

Answer:

The solution of the equation is $x=\frac{(ln4)-5}{2}$ ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to solve this problem

- The function f(x) = e^x is called the (natural) exponential function

- The natural logarithm (㏑), or logarithm to base e, is the inverse

 function to the natural exponential function

∵ $e^{2x+5}=4$ is an exponential function

∴ We can solve it by using the inverse of e (㏑)

- Remember:

# $ln(e)=1$

# $ln(e^{m})=m(ln(e))=m$

- Insert ln in both sides

∴ $ln(e^{2x+5})=ln(4)$

∵ $ln(e^{2x+5})=(2x+5)ln(e)=2x+5$

∴ 2x + 5 = ㏑(4)

- Subtract 5 from both sides

∴ 2x = ㏑(4) - 5

- Divide both sides by 2 to find x

∴ $x=\frac{ln(4)-5}{2}$

* The solution of the equation is $x=\frac{(ln4)-5}{2}$