Question

if ³√32=2x then x is equal to​

Answer 1

Answer:

Let x is equal to n

2ⁿ=3 root 32

2ⁿ=2 5/3

n=5/3

x=5/3

Answer 2

Answer:

Concept:

The Power Rule of Exponents:

• To raise a number with an exponent, multiply the exponent by the power.
• The formula for the exponent power rule is

             $(x^a)^b = x^{a*b}$

Cube Root:

• In order to obtain a given number, we multiply the cube root of that number three times.
• Cube root is represented by  "3 cube root of".
• Cube root of y ($\sqrt[3]{y}$) is also written as $y^{\frac{1}{3} }$.
• The opposite of cubing a number is determining its cube root.

Given:

$\sqrt[3]{32} = 2^x$

To Find:

We need to find the value of x.

Solution:

Here,

$2^1=2$

$2^2=2*2=4$

$2^3= 2*2*2=8$

$2^4=2*2*2*2=16$

$2^5=2*2*2*2*2=32$

From the above expression we know that $2^5=32$,

⇒  $2^x= \sqrt[3]{32}$

⇒  $2^x= (32)^{\frac{1}{3} }$

⇒  $2^x = (2^5)^{\frac{1}{3}}$

By using the power rule of exponent,

⇒  $2^x = (2)^{5*\frac{1}{3}}$

⇒  $2^x = (2)^{\frac{5}{3}}$

⇒  $x=\frac{5}{3}$

Therefore, the value of $x = \frac{5}{3}$

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