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What is the value of x in the equation below 1+2e^x+1=9

User Ricardo
by
8.0k points

2 Answers

5 votes

Answer:


x=1.2528

Explanation:

Assuming the equation to solve is


1+2e^x+1=9

We can first simplify as:


1+2e^x+1=9\\2+2e^x=9\\2e^x=9-2\\2e^x=7\\e^x=(7)/(2)

to solve an equation with e and x as an exponent, we need to take "natural log (ln)" on both sides and also use the property:


ln(a^x)=xln(a)

And also remember that ln e = 1

Now we have:


e^x=(7)/(2)\\ln(e^x)=ln((7)/(2))\\xln(e)=ln((7)/(2))\\x(1)=ln((7)/(2))\\x=ln((7)/(2))\\x=1.2528

User Foobarometer
by
8.6k points
4 votes

Answer:
x
1.252

Explanation:

Given the equation
1+2e^x+1=9, add the like terms:


2e^x+2=9

Subtract 2 from both sides:


2e^x+2-2=9-2


2e^x=7

Divide both sides by 2:


(2e^x)/(2)=(7)/(2)\\\\e^x=(7)/(2)

Apply natural logarithm to both sides. Remember that


ln(e)=1 and
ln(m)^n=nln(m)

Then, you get:


ln(e)^x=ln((7)/(2))\\\\xln(e)=ln((7)/(2))\\\\x=ln((7)/(2))


x
1.252

User Marco Scabbiolo
by
7.9k points

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