Question

Find x. Please help?

Answer 1

Solution:

To Determine :- The value of x.

Given Equation :-

$\rm \implies \dfrac{ {2}^{3x + 1} }{ {3}^{4} } \times {3}^{5} = 48$

Can be written as :-

$\rm \implies {2}^{3x + 1} \times {3}^{5 - 4} = 48$

$\rm \implies {2}^{3x + 1} \times {3}^{1} = 48$

$\rm \implies {2}^{3x + 1} \times3 = 48$

Dividing both sides by 3, we get :-

$\rm \implies {2}^{3x + 1} =48 \div 3$

$\rm \implies {2}^{3x + 1} =16$

$\rm \implies {2}^{3x + 1} = {2}^{4}$

Comparing base, we get :-

$\rm \implies 3x + 1 = 4$

$\rm \implies 3x = 3$

$\rm \implies x = 1$

→ Therefore, the value of x in this equation is 1.

Learn More:

Laws of Exponents.

$\rm 1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\rm 2. \: \: ({a}^{m})^{n} = {a}^{mn}$

$\rm 3. \: \: \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\rm4. \: \: {a}^{m} \times {b}^{m} = {(ab)}^{m}$

$\rm5. \: \: \bigg(\dfrac{a}{b} \bigg)^{m} = \dfrac{ {a}^{m} }{ {b}^{m} }$

$\rm6. \: \: {a}^{ - n} = \dfrac{1}{ {a}^{n} }$

$\rm7. \: \: {a}^{n} = {b}^{n} \rightarrow a = b, n \neq0$

$\rm8. \: \: {a}^{m} = {a}^{n} \rightarrow m = n, a \neq 1$

Answer 2

Answer:

Value of x = 1

Step-by-step explanation:

Well, just some very basic exponential question. You are needed to know the properties of exponential,else I swear these questions can be nightmare when the level of the question rises in ahead in the chapter,this one is still a very simple and basic one. Let's see how to solve.

=> 2⁽³ˣ ⁺ ¹⁾ × 3⁵ / 3⁴ = 48

Now you should be knowing :

=> aˣ/aʸ

= aˣ × a⁻ʸ

= a ⁽ˣ ⁻ ʸ⁾

Using this :

=> 2⁽³ˣ ⁺ ¹⁾ × 3⁵ × 3⁽⁻⁴⁾ = 48

=> 2⁽³ˣ ⁺ ¹⁾ × 3¹ = 48 [∵ 3⁵⁻ ⁴ = 3¹]

=> 2⁽³ˣ ⁺ ¹⁾ × 3 = 48

=> 2⁽³ˣ ⁺ ¹⁾ = 48/3

=> 2⁽³ˣ ⁺ ¹⁾ = 16

Now we can represent 16 in the form of base 2 and power 4,so that we can directly compare the powers.

=> 2⁽³ˣ ⁺ ¹⁾ = 2⁴

Since the base are same,we just need to care about equating the power.

=> 3x + 1 = 4

=> 3x = 4 -1

=> 3x = 3

=> x = 1