Solving Logarithmic Equations

Hi guys, it's Nicole and this post is about solving the logarithmic equations.

Steps:

1. Simplify the equation to create a proper logarithmic form. Use the laws of logarithms where appropriate to create a single logarithm in proper form.

• In other words, make sure that the equation follows the format:

2. Convert the logarithm into exponential form.

• since your equation is in logarithmic form, use the 7-rule.

3. Solve the resulting equation for the missing variable.

• if the variable is the exponent, make the bases the same. That way, you can cancel the bases and find x.

• if the variable is the base, make the exponents the same. Same rule also applies to this one. you can cancel the exponents and find x.

4. Check your answer(s). Remember that you cannot evaluate the logarithm of a negative number of zero. plug your answer(s) back into the original equation and check! 

Here's another example. This time, the logarithm has a coefficient.

  

This one has 2 logarithmic functions

and again, check your answers! x cannot be a negative nor zero. 

remember to plug your answers back into the original equation.

That's it guys, it wasn't that hard, wasn't it?