C25 - solving problems involving exponential and logarithmic equations

 

 

Lindsay

 

Definitions:

 

Exponential Equation: an equation involving an exponential function of a variable

 

Example:

 

What this is saying: 3 to the power of x is equal to 27.

 

 

Logarithmic Equation: an equation involving a log function of a variable

 

Example:

 

What this is saying: 3 to the power of x is equal to 27.

 

 

They say the same thing?!

 

Yes!! They say the same thing because they are the same thing!

 

=

 

How to convert from an exponential equation to a logarithmic eqaution:

 

First, let's indentify the parts of an each equation:

 

 

The 3 is the BASE. The x is the EXPONENT. The 27 is the SOLUTION.

 

To make this a logarithm, you have to change some things around.

 

The BASE of a logarithmic equation is the same BASE from the exponential equation, but the EXPONENT and SOLUTION change places.

 

The 3 is still the BASE. The 27 is now called the ARGUEMENT. The x is the SOLUTION.

 

To solve a logarithmic equation: Since a calculator will only do logarithms of log base 10, you need to use the CHANGE OF BASE formula. This is taking the log base 10 of the ARGUEMENT divided by the log base 10 of the BASE. The answer you'll get will equal x.

 

Example:

 

 

Now try some on your own!! I'll give examples of changing from an exponential equation to a logaritmic equation and back. Solve for x in each question.

 

 

 

 

 

Answers:

 

a) x=4  b) x=2  c) x=6  d) x=4096  e) x=216