Answer:
The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex] ⇒ 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
∵ [tex]e^{2x+5}=4[/tex] is an exponential function
∴ We can solve it by using the inverse of e (㏑)
- Remember:
# [tex]ln(e)=1[/tex]
# [tex]ln(e^{m})=m(ln(e))=m[/tex]
- Insert ln in both sides
∴ [tex]ln(e^{2x+5})=ln(4)[/tex]
∵ [tex]ln(e^{2x+5})=(2x+5)ln(e)=2x+5[/tex]
∴ 2x + 5 = ㏑(4)
- Subtract 5 from both sides
∴ 2x = ㏑(4) - 5
- Divide both sides by 2 to find x
∴ [tex]x=\frac{ln(4)-5}{2}[/tex]
* The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex]
