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Coolmath Algebra
Exponentials & Logarithms Lesson 11 - Solving Exponential Equations  (page 1 of 4)
---- This algebra lesson explains how to solve exponential equations

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So far, we've been solving equations like
 
2x - 5 = 7 and x^( 2 ) - 3x - 10 = 0

(a linear equation)

 

(a quadratic equation)

But, NOW the unknown is going to be in the exponent!

Check it out:

Solve   5 = e^( 7t )

We need a way to get to the t...  We HAVE to solve for Mr. t.  I pity the fool who can't solve Mr. t !  Pity the fool!  (Sorry for the lame A-Team joke.)

5 = e^( 7t )

Who is in the way?

e !

How can we ditch that e?  Can you think of anything that will undo it?

The natural log!  He's an e killer!

Just remember... 
Anything we do to one side of an equation,
we have to do to the other!

 

So...  take the natural log of each side:

5 = e^( 7t ) ... Ln( 5 ) = Ln( e^( 7t ) ) ... Ln( 5 ) = 7t ... Ln( 5 ) / 7 = 7t / 7 ... Ln( 5 ) / 7 = t ... the Ln undoes the e

So, t = Ln( 5 ) / 7

You can pop this into your calculator...

t = approximately .2299

(Four decimal spots is OK.)

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.

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