Problem 137
Question
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because the equations \(2^{x}=15\) and \(2^{x}=16\) are similar, I solved them using the same method.
Step-by-Step Solution
Verified Answer
Yes, the statement makes sense. Despite the fact that the values on the right hand side of the equations are different, the equations are similar and can be solved using the same method, which is typically done using logarithms.
1Step 1: Analyze the equations
By examining both equations, it can be seen that they have the same base on the left hand side - which is 2. Furthermore, the exponential variable is also the same in both equations. Therefore, both equations do have similar structural format.
2Step 2: Evaluate the reasoning
The given reasoning is that since the equations are similar, they are solved using the same method. This reasoning is valid because irrespective of the difference in right hand side values, the general method of solving exponential equations remains the same - that is, by applying logarithmic operations.
3Step 3: Conclusion
The statement given in the question does make sense. Although the equations are not identical, they are similar as they follow the same equation structure and hence can be solved using the same method.
Other exercises in this chapter
Problem 136
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