Question

If 3x−y=12, what is the value of
$= \frac{ {8}^{x} }{ {2}^{y} }$


A) 2¹²
B) 4⁴
C) 8²
D) The value cannot be determined from the information given.​

Answer 1

$\huge \color{blue}Question :-$

If 3x−y=12, what is the value of

$= \frac{ {8}^{x} }{ {2}^{y} }$

A) 2¹²

B) 4⁴

C) 8²

D) The value cannot be determined from the information given.

$\huge \color{lime}Answer :-$

Since 2 and 8 are both powers of 2 .

2³ for 8

• So numerator -

$\frac{8 {}^{x} }{2 {}^{y} }$

So we can write it as -

$\frac{(2 {}^{3}) {}^{x} }{2 {}^{y} } \\ \\ \frac{2 {}^{3}x }{2 {}^{y} }$

• Since numerator and denominator have common base.

• So we can write

$2(3x - y) \\ \\ 3x - y = 12$

So,

$\frac{8x}{2y} = 2 {}^{12}$

Option A) is correct

$\huge \color{orange}Hope \: it \: is \: helpful$

Answer 2

EXPLANATION.

⇒ 3x - y = 12.

As we know that,

To find :

⇒ 8^(x)/2^(y).

We can write equation as,

⇒ 2^(3x)/2^(y).

⇒ 2^(3x - y).

Put the value of 3x - y = 12 in the equation, we get.

⇒ 2¹².

Hence option [A] is correct answer.

                                                                                                                             

MORE INFORMATION.

Properties of logarithms.

Let M and N arbitrary positive number such that a > 0, a ≠ 1, b > 0, b ≠ 1 then,

(1) = ㏒ₐMN = ㏒ₐM + ㏒ₐN.

(2) = ㏒ₐ(M/N) = ㏒ₐM - ㏒ₐN.

(3) = ㏒ₐN^(α) = α㏒ₐN, (α any real number).

(4) = ㏒ₐ^(β)N^(α) = α/β㏒ₐN, (α ≠ 0, β ≠ 0).

(5) = ㏒ₐN = ㏒_{b}N/㏒_{b}a.

(6) = ㏒_{b} a. ㏒ₐb = 1 ⇒ ㏒_{b}a = 1/㏒ₐb.

(7) = e^(㏑a)ˣ = aˣ.