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

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

Answer/Discussion to 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.

*Take the natural log of BOTH sides

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

*Use the power rule

Step 4: Solve for x.

*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)

Answer/Discussion to 1b

Step 1: Isolate the exponential expression.

*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.

*Take the natural log of BOTH sides

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

*Use the power rule

Step 4: Solve for x.

*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)

Answer/Discussion to 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 .

*Factor the trinomial of the form .

*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 .

Step 2: Take the natural log of both sides.

*Take the natural log of BOTH sides

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

*Use the power rule

Step 4: Solve for x.

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

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

(return to problem 1c)

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

Last revised on March 23, 2011 by Kim Seward.
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