Exponential and Logarithmic Equations

Pre-Calculus Tutorial

Exponential and Logarithmic Equations


Exponential and Logarithmic equations are very simple; however, algebraic mistakes can easily be made. This problem illustrates how to find the solution set in terms of “e” and the solution set in decimal form.

Sample Problem

Find the solution set in terms of “e” and in decimal form.


We are given 2ln(6x)=8

-The first thing the question asks is for the solution set in terms of “e”
-All that means is solve for x


2ln(6x)/2=8/2 -We divide by two on both sides

ln(6x)=4 -The 2 on the left side cancels out and on the right divides to 4

-our initial reaction is to divide the 6 on both sides, DO NOT! We have to think of the ‘ln’ and the ‘6x’ as married and in order to separate them we must get rid of the ‘ln’
-in order to get rid of the ‘ln’ we exponentiate both sides with base “e.”

e^ln(6x)= e^4

Then the “ln” and the “e” cancel out


Now we may divide the 6 on both sides and we are left with

x=e^4/6 ==> and this is our solution set in terms of “e”

Our solution set in decimal form is simply the quotient of e^4/6 which is 9.10

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