From the previous question- 22 a-1- 23 b-2-62-6 C-with a- b and c as whole numbers- you have simplified the left hand side of the equation to 2x- 3y- where x-2 a-1 and y-3 b- Choose the correct option which relates a and b with c-A- 2 a -1- cB- 3 b-cC- Both A and BD- None of the above

The correct option is C Both A and B Since 2^x × 3^y = 6^c ⇒ 2^x × 3^y = (2 × 3)^c = 2^c × 3^c , we must have x = c = 2a – 1 and c = y = 3b and hence both A an ...

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Byju's Answer

Standard VII

Mathematics

Expression Formation

From the prev...

Question

From the previous question,

$\frac{2^{(2 a + 1)} \times 2^{(3 b + 2)}}{6^{2}} = 6^{c}$

,with a, b and c as whole numbers, you have simplified the left hand side of the equation to 2^x x 3^y, where x = 2a – 1 and y = 3b.

Choose the correct option which relates a and b with c.

2a – 1 = c

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3b = c

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Both A and B

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None of the above

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Solution

The correct option is C
Both A and B

Since $2^{x} \times 3^{y} = 6^{c} \Rightarrow 2^{x} \times 3^{y} = (2 \times 3)^{c} = 2^{c} \times 3^{c}$ , we must have x = c = 2a – 1 and c = y = 3b and hence both A and B are correct.

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Similar questions

If $\frac{2^{(2 a + 1)} \times 3^{(3 b + 2)}}{6^{2}} = 2^{x} \times 3^{y}$

Chose the correct option:

In the previous question, if only b = 0 and a is nonzero, the LHS becomes odd. Say True or False.

[The equation is $2^{a} + 3^{b}$ = 4 and a, b are whole numbers]

Q. Question 13
Find and correct the errors in the statement:

(2 a + 3 b) (a - b) = 2 a^{2} - 3 b^{2}

Q. If

2^{a} = 3^{b} = 6^{c}

, then

c =

Q. If

2^{a} + 3^{b} = 17

and

2^{a + 2} - 3^{b + 1} = 5,

then find the value of a and b.

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From the previous question, 2(2a+1)×2(3b+2)62=6c ,with a, b and c as whole numbers, you have simplified the left hand side of the equation to 2x x 3y , where x = 2a – 1 and y = 3b. Choose the correct option which relates a and b with c.

The correct option is C Both A and B Since 2x×3y=6c⇒2x×3y=(2×3)c=2c×3c , we must have x = c = 2a – 1 and c = y = 3b and hence both A and B are correct.

From the previous question,

$\frac{2^{(2 a + 1)} \times 2^{(3 b + 2)}}{6^{2}} = 6^{c}$

,with a, b and c as whole numbers, you have simplified the left hand side of the equation to 2^x x 3^y, where x = 2a – 1 and y = 3b.

Choose the correct option which relates a and b with c.

The correct option is C
Both A and B

Since $2^{x} \times 3^{y} = 6^{c} \Rightarrow 2^{x} \times 3^{y} = (2 \times 3)^{c} = 2^{c} \times 3^{c}$ , we must have x = c = 2a – 1 and c = y = 3b and hence both A and B are correct.