Solving exponential equations by taking the log of both sides.

1. Base 10 and Other Base systems:
• During the Exponents Unit we saw how to solve
exponential equations. For example:
• To solve these types of problems we needed to
obtain a like base.
• Once the bases where like then I can set the
exponents equal to each other.
3x = 3
x = 1
• Today we are going to learn how to solve problems
where obtaining a like base is very difficult. So we
need another way to solve those types of problems.
1

2. Base 10 ­
Ex ­ Solve for x:
As you can see it would be very hard to rewrite this
equation with like bases. Therefore the steps we will
use to solve this type of problem are:
Step1 ­ Convert to logarithm.
Step 2 ­ Solve by using graphing calculator
Type in log253 = 2.4
Practice, Solve for x:
Step 1 ­ Convert to logarithm.
Step 2 ­ Solve by using graphing calculator
Type in log10000 = 4
2

3. 3

4. Not­Base 10 ­
Ex ­ Solve for x:
Using the steps from the previous problem:
1st ­ Convert to logarithm.
2nd ­ There's a problem. Since the equation is not
base 10 system, you cannot use your calculator to solve
it.
Our solution is to take the log of both sides of the
exponential equation. This converts the entire
equation to base 10 instead of base 3.
original problem:
step 1: log 3x = log 47
Step 2: Now using the laws of logarithms rewrite the
equation:
x log 3 = log 47
Step 3 : Get x by itself:
x = log 47
log 3
Step 4: Now you can use your calculator to solve.
x = 3.5
4

5. Now try this one: 9x = 14
5

6. 2. 2x = 21
6

7. x
3. 4 = 67
7

8. 4. 102x = 3.5
8

9. 5. 23x = 7
9