Question

if 2 power x multiply 4 power x is equal to 8 power 1 by 3 into 32 power 1 by 5 then find the value of x​

Answer 1

Step-by-step explanation:

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Answer 2

Given,

An equation, $(2^{x} )(4^{x} ) = (8^{\frac{1}{3} })(32^{\frac{1}{5} } )$

To Find,

The value of $x$.

Solution,

Given,

$(2^{x} )(4^{x} ) = (8^{\frac{1}{3} })(32^{\frac{1}{5} } )$

To equate the powers, all the bases must be equal.

Therefore, convert all the bases in the given equation into exponents of 2.

⇒$(2^{x} )((2^{2} )^{x} ) = ((2^{3}) ^{\frac{1}{3} })((2^{5}) ^{\frac{1}{5} } )$

On simplification,

⇒$(2^{x} )((2^{2x} ) = (2^{(3)(\frac{1}{3}) } )(2^{(5)(\frac{1}{5}) } )$

On further simplification,

⇒$2^{(x+2x)} = (2^{1 } )(2^{1 } )$

⇒$2^{(x+2x)} = 2^{(1+1) }$

⇒$2^{(3x)} = 2^{2 }$

Since bases are equal, we can equate the exponents.

Therefore, $3x = 2$

⇒$x = \frac{2}{3}$

Henceforth, the value of $x$ is $\frac{2}{3}$.