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I see all the time kids asking about the same questions so I will create this as to reference when basic methodology is needed to be taught
To start off basic exponent rules:
...NOTE
Using this in conjunction with the second rule we can see that
Now I will move onto logarithmic properties
NOTE: is used in lieu of other logarithims for its shortness....these rules apply to all logarithims...and for knowledge
and
A very important one for solving equations as well as using a calculator is the change of base theorem which states
Most useful example is
another thing you should know is
Now I will go over the way to solve two basic logarithmic equations
Case 1...this is one with a pre-existing log
first combien the logs to get
we want to isolate the x so we introduce the exponential function( ) to eliminate the log
so we have
taking the squareroot of both sides and using rules 5 and 6 in the exponent section we see the answer is
Case 2....introducing logs to eliminate exponents...
First thing we want to do is introduce a log to elminate the exponent...the log we introduce is always of same base as the exponent in this case 8..so we have
at this point I think it is prudent to discuss extraneous solutions
is defined only for positive values for x...so you might get an algaebraic solution that works but it makes a log undefined..these solutiong are to be discarded
any questions just ask