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What are the different approaches and methods you have used to solve other types of equations?
See solution.
There are different ways to solve exponential and logarithmic equations. Just as with other type of equations, there is a graphical, numerical, and an analytical approach. We will explain an example method for each case.
The solution to this equation is x =- 3.
Another way to solve these type of equations is by doing a table of values. Let's consider a different equation this time. 16^x -2 = 0
x | 16^x-2 |
---|---|
-1 | 16^(- 1) -2 = -1.9375 |
- 0.5 | 16^(- 0.5) -2 = -1.75 |
0 | 16^0 -2 = -1 |
0.5 | 16^(0.5) -2 = 2 |
1.5 | 16^(1.5) -2 = 62 |
2 | 16^2 -2 = 254 |
We can see that the solution happens somewhere between 0 and 0.5, as there is a change of sign from one value to the other. To give a more precise answer we can do the x-intervals smaller and evaluate between those values where we know our answer should be.
x | 16^x-2 |
---|---|
0 | 16^0 -2 = -1 |
0.25 | 16^(0.25) -2 = 0 |
0.5 | 16^(0.5) -2 = 2 |
As we can see, the solution to our equation is x=0.25. If we had not found the solution once more, we can repeat the process using smaller intervals until we find the solution, or until we can give an approximate answer that is good enough for our purpose.
LHS+2=RHS+2
log_(16)(LHS)=log_(16)(RHS)
log_(16)(16^m)=m
Use a calculator