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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Surds and Indices" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
(17)3.5 x (17)? = 178
- a)2.29
- b)2.75
- c)4.25
- d)4.5
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
Let (17)3.5 x (17)x = 178
Then, (17)3.5 + x = 178
∴ 3.5 + x = 8
⇒ x = (8 - 3.5)
⇒ x = 4.5
Then, (17)3.5 + x = 178
∴ 3.5 + x = 8
⇒ x = (8 - 3.5)
⇒ x = 4.5
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
By LAW OF INDICES :-
(a)^m × (a)^n = a^(m+n)
i.e., During MULTIPLICATION ,when bases (a&a) are common , we can add the powers. so ,
(17)^3.5 × (17)^x = (17 )^8
17^(3.5+x) = (17 )^8
When we have same base on both sides , we can equate it as follows:-
3.5+x= 8; x= 8-3.5;
Hence , x = 4.5 .
(a)^m × (a)^n = a^(m+n)
i.e., During MULTIPLICATION ,when bases (a&a) are common , we can add the powers. so ,
(17)^3.5 × (17)^x = (17 )^8
17^(3.5+x) = (17 )^8
When we have same base on both sides , we can equate it as follows:-
3.5+x= 8; x= 8-3.5;
Hence , x = 4.5 .
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
Solution:
Given equation: (17)3.5x = 178
To solve this equation, we need to isolate the variable x on one side of the equation.
Step 1: Simplify the equation
We can simplify the equation by evaluating the expression (17)3.5x.
(17)3.5x can be written as (17)(3.5)(x).
Multiplying 17 and 3.5, we get 59.5. So, the equation becomes:
59.5x = 178
Step 2: Solve for x
To solve for x, we need to isolate it on one side of the equation.
Divide both sides of the equation by 59.5:
59.5x/59.5 = 178/59.5
x = 178/59.5
Step 3: Simplify the division
Dividing 178 by 59.5, we get:
x ≈ 2.99
Therefore, the value of x is approximately 2.99.
Now let's check which option satisfies the given equation.
Option A: 2.29
(17)3.5(2.29) = 17*3.5*2.29 = 137.29
Option B: 2.75
(17)3.5(2.75) = 17*3.5*2.75 = 166.375
Option C: 4.25
(17)3.5(4.25) = 17*3.5*4.25 = 251.875
Option D: 4.5
(17)3.5(4.5) = 17*3.5*4.5 = 267.75
Comparing the results of the options with the given equation, we can see that only option D, 4.5, satisfies the equation.
Therefore, the correct answer is option D, 4.5.
Given equation: (17)3.5x = 178
To solve this equation, we need to isolate the variable x on one side of the equation.
Step 1: Simplify the equation
We can simplify the equation by evaluating the expression (17)3.5x.
(17)3.5x can be written as (17)(3.5)(x).
Multiplying 17 and 3.5, we get 59.5. So, the equation becomes:
59.5x = 178
Step 2: Solve for x
To solve for x, we need to isolate it on one side of the equation.
Divide both sides of the equation by 59.5:
59.5x/59.5 = 178/59.5
x = 178/59.5
Step 3: Simplify the division
Dividing 178 by 59.5, we get:
x ≈ 2.99
Therefore, the value of x is approximately 2.99.
Now let's check which option satisfies the given equation.
Option A: 2.29
(17)3.5(2.29) = 17*3.5*2.29 = 137.29
Option B: 2.75
(17)3.5(2.75) = 17*3.5*2.75 = 166.375
Option C: 4.25
(17)3.5(4.25) = 17*3.5*4.25 = 251.875
Option D: 4.5
(17)3.5(4.5) = 17*3.5*4.5 = 267.75
Comparing the results of the options with the given equation, we can see that only option D, 4.5, satisfies the equation.
Therefore, the correct answer is option D, 4.5.
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for"Surds and Indices"under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.(17)3.5x (17)?= 178a)2.29b)2.75c)4.25d)4.5Correct answer is option 'D'. Can you explain this answer?
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