Solving Exponential Equations Using Logarithms
In order to solve you need to use .
Exponential equations with base 10
The following method is used to solve exponential equations where the powers have a base-10, like for example
Solve for the power of ten that includes the unknown variable
Solve for the power with the unknown variable so that it is by itself on either the right or left hand side.
Take the log of both sides
By using log on the both sides and simplifying, you can separate out the variable so that it is along on one side of the equation.
This is the for the equation. However, if you are not asked for the exact answer, you can get an approximate one by entering
into your calculator:
General exponential equations
Exponential equations with bases, like , for example, can be solved using .
Solve for the power that contains the unknown variable
Solve for the term that includes the power with the unknown variable so that it stands alone on one side.
Take the logarithm of both sides
Take the logaritm of the left and right hand sides.
Pull down the exponent and place it in front of the logarithm.
Solve for the variable by dividing by the logarithm.
This is the answer in its , and if you enter it into your calculator you will get the approximate answer