Question

Find the value of x if 4^3 3^3 = (4x)^3.

Answer 1

Step-by-step explanation:

64

$\times$

27

1728=64x^3

x^3=1728/64

x=3

Answer 2

The correct answer is x=1.

Given:

4³. 3³ = (4x)³

To Find:

The value of x.

Solution:

To solve this question, we need to understand the basic rules of exponentiation.

If n is a positive integer and a is any real number, the:

$a^{n}$ = a x a x...a (n times).

Here, a is called the base, and n is called the exponent or power.

Let us assume that x, y, a, and b are integers.

1) Product of exponentials having the same base:

$x^{a} . x^{b} = x^{(a+b)}$

2) Quotient of exponentials with the same base:

$\frac{x^{a}} { x^{b}} = x^{(a-b)}$, x≠0.

3) The power of power:

$(x^{a})^{ b} = x^{ab}$

4) The power of a product:

$(xy)^{a} = x^{a}.x^{b}$

Now, we are given 4³. 3³ = (4x)³. From rule 4, the LHS of the given equation becomes:

4³. 3³ = (4.3)³

Hence, the equation becomes:

(4.3)³ = (4x)³.

On comparing both sides, we get x=1.

∴ The correct answer is x=1.

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