College Algebra Tutorial 45


College Algebra
Answer/Discussion to Practice Problems  
Tutorial
45: Exponential Equations


WTAMU > Virtual Math Lab > College Algebra > Tutorial 45: Exponential Equations


 

checkAnswer/Discussion to 1a

problem 1a
 

Step 1: Isolate the exponential expression.

 
This is already done for us in this problem.

 
Step 2: Take the natural log of both sides.

 
ad1a1
*Take the natural log of BOTH sides

 
Step 3: Use the properties of logs to pull the x out of the exponent.

 
ad1a2
*Use the power rule

 
Step 4: Solve for x.

 
ad1a3

*Inverse of mult. by lne is to divide by lne
 
 
 

*Inverse of sub. 1 is add. 1
 
 
 
 

*Inverse of mult. by .5 is divide by .5
 

*Use the calculator to find ln 20
*lne is 1

 
 

(return to problem 1a)


 

checkAnswer/Discussion to 1b

problem 1b
 

Step 1: Isolate the exponential expression.

 
ad1b1
*Inverse of sub. 7 is add 7
 

*Inverse of mult. by 4 is to divide by 4
 

*Exponential expression isolated
 
 

Step 2: Take the natural log of both sides.

 
ad1b2
*Take the natural log of BOTH sides

 
Step 3: Use the properties of logs to pull the x out of the exponent.

 
aad1b3
*Use the power rule

 
Step 4: Solve for x.

 
ad1b4

*Inverse of mult. by ln 10 is to divide by ln 10
 

*Use the calculator to find ln 25.5 and ln 10
 
 

 
 

(return to problem 1b)


 

checkAnswer/Discussion to 1c

problem 1c
 
 

Step 1: Isolate the exponential expression.

 
Notice how we have two exponential terms that have different exponents.  We wouldn't be able to isolate both.  We will have to figure out another way to rewrite it so we can continue with the steps. 

Note how we have a trinomial and that e to the 2x is e to the x squared.  This means it is quadratic in from.  So we can factor it just like a trinomial of the form example 4b.
 

ad1c1

*Factor the trinomial of the form example 4b.
 

*Set the 1st factor = 0
*Isolate the exponential expression
 
 
 
 

*Set the 2nd factor = 0
*Isolate the exponential expression
 
 

Note that since e is a positive base, no matter what the exponent is on x, this exponential expression CANNOT equal -3.

So there is only one equation that we can solve ad1c2.
 
 

Step 2: Take the natural log of both sides.

 
ad1c3
*Take the natural log of BOTH sides

 
Step 3: Use the properties of logs to pull the x out of the exponent.

 
ad1c4
*Use the power rule

 
Step 4: Solve for x.

 
ad1c5
*Inverse of mult. by lne is to divide by lne
 
 
 

*Use the calculator to find ln 7
*lne = 1

 
 

(return to problem 1c)

 

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WTAMU > Virtual Math Lab > College Algebra > Tutorial 45: Exponential Equations


Last revised on March 23, 2011 by Kim Seward.
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