College Algebra Tutorial 46


College Algebra
Answer/Discussion to Practice Problems  
Tutorial
46: Logarithmic Equations


WTAMU > Virtual Math Lab > College Algebra > Tutorial 46: Logarithmic Equations


 

checkAnswer/Discussion to 1a

problem 1a
 

Step 1:  Write as one log isolated on one side.

 
This is already done for us in this problem.

 
Step 2: Use the definition of logarithms to write in exponential form.

 
cad1a1
*Rewrite in exponential form
*Base = 10 and exponent = 3

 
Remember that when there is no base written on a log, that means it is the common log, or log base 10.  If you need a review on common logs feel free to go to Tutorial 43: Logarithmic Functions.

 
Step 3: Solve for x.

 
ad1a2

*10 cubed is 1000
*Solve for x
 
 

 
 

(return to problem 1a)


 

checkAnswer/Discussion to 1b

problem 1b
 

Step 1:  Write as one log isolated on one side.

 
adb1

*Use the product rule to write as one log
*one log is isolated

 
Step 2: Use the definition of logarithms to write in exponential form.

 
ad1b2
*Rewrite in exponential form
*Base = 2 and exponent = 4

 
Step 3: Solve for x.

 
ad1b3

*2 to the 4th power is 16
*Solve for x

*Factor the trinomial

*Set 1st factor = 0 
 
 
 
 

*Set 2nd factor = 0 

 
 

Since -2 would create a negative number inside both logs in this problem and we CANNOT take the log of a negative number, we will have to throw out x = -2 as one of our solutions.
 

Final answer: x = 8.
 

(return to problem 1b)


 

checkAnswer/Discussion to 1c

problem 1c
 

Step 1:  Write as one log isolated on one side.

 
ad1c1

*Use the quotient rule to write as one log
*one log is isolated

 
Step 2: Use the definition of logarithms to write in exponential form.

 
ad1c2
*Rewrite in exponential form
*Base = 4 and exponent = 2

 
Step 3: Solve for x.

 
ad1c3

*4 squared is 16
*Solve for x
 

*Multiply both sides by LCD of x - 1
 
 
 
 
 
 
 
 
 

 
 

The equation that we had to solve in step 3 had a rational expression in it.  If you need a review on solving equations with rational expressions feel free to go to Tutorial 15: Equations with Rational Expressions.

 
(return to problem 1c)


 

checkAnswer/Discussion to 1d

problem 1d
 

Step 1:  Write as one log isolated on one side.

 
ad1d1

*Inverse of add 5 is sub. 5

*one log is isolated
 

Step 2: Use the definition of logarithms to write in exponential form.

 
ad1d2
*Rewrite in exponential form
*Base = e and exponent = 1

 
Remember that when you have ln, that means it is the natural log, or log base e.  If you need a review on natural logs feel free to go to Tutorial 43: Logarithmic Functions.

 
Step 3: Solve for x.

 
ad1d3

*Square both sides to get rid of the radical

*Solve for x
 

*Use the calculator to find e squared
 

 
 

The equation that we had to solve in step 3 had a square root in it.  If you need a review on solving equations with radicals feel free to go to Tutorial 19: Radical Equations and Equations Involving Rational Exponents.

 
(return to problem 1d)

 

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WTAMU > Virtual Math Lab > College Algebra > Tutorial 46: Logarithmic Equations


Last revised on March 23, 2011 by Kim Seward.
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