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If 3^m =81 then find the value of 7^2m-8?
Most Upvoted Answer
If 3^m =81 then find the value of 7^2m-8?
Step 1: Solve for m
To find the value of m, we start with the equation:
- 3^m = 81
Next, we can express 81 as a power of 3:
- 81 = 3^4
Now, we can equate the exponents since the bases are the same:
- m = 4
Step 2: Calculate 2m
Now that we have found m, we can calculate 2m:
- 2m = 2 * 4 = 8
Step 3: Find the value of 7^(2m - 8)
Next, we need to substitute the value of 2m into the expression 7^(2m - 8):
- 2m - 8 = 8 - 8 = 0
Now, we can simplify the expression:
- 7^(2m - 8) = 7^0
Step 4: Evaluate 7^0
Any non-zero number raised to the power of 0 is equal to 1:
- 7^0 = 1
Final Answer
Thus, the value of 7^(2m - 8) is:
- 1
In summary, by determining m from the original equation, calculating 2m, and substituting into the expression, we found that the final result is 1.
To find the value of m, we start with the equation:
- 3^m = 81
Next, we can express 81 as a power of 3:
- 81 = 3^4
Now, we can equate the exponents since the bases are the same:
- m = 4
Step 2: Calculate 2m
Now that we have found m, we can calculate 2m:
- 2m = 2 * 4 = 8
Step 3: Find the value of 7^(2m - 8)
Next, we need to substitute the value of 2m into the expression 7^(2m - 8):
- 2m - 8 = 8 - 8 = 0
Now, we can simplify the expression:
- 7^(2m - 8) = 7^0
Step 4: Evaluate 7^0
Any non-zero number raised to the power of 0 is equal to 1:
- 7^0 = 1
Final Answer
Thus, the value of 7^(2m - 8) is:
- 1
In summary, by determining m from the original equation, calculating 2m, and substituting into the expression, we found that the final result is 1.
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If 3^m =81 then find the value of 7^2m-8?
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If 3^m =81 then find the value of 7^2m-8? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 3^m =81 then find the value of 7^2m-8? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 3^m =81 then find the value of 7^2m-8?.
If 3^m =81 then find the value of 7^2m-8? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 3^m =81 then find the value of 7^2m-8? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 3^m =81 then find the value of 7^2m-8?.
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