Question

If (2x-3)the power of 2=xth power of 64,find the value of x

Answer 1

Answer:

The value of x is

$\displaystyle{\boxed{\red{\sf\:x\:=\:-\:\dfrac{3}{4}\:}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:2^{(\:2x\:-\:3\:)}\:=\:64^x}$

We have to find the value of x.

Now,

$\displaystyle{\sf\:2^{(\:2x\:-\:3\:)}\:=\:64^x}$

$\displaystyle{\implies\sf\:2^{(\:2x\:-\:3\:)}\:=\:(\:8^2\:)^x}$

$\displaystyle{\implies\sf\:2^{(\:2x\:-\:3\:)}\:=\:8^{2x}}$

$\displaystyle{\implies\sf\:2^{(\:2x\:-\:3\:)}\:=\:(\:2^3\:)^{2x}}$

$\displaystyle{\implies\sf\:2^{(\:2x\:-\:3\:)}\:=\:2^{3\:\times\:2x}}$

$\displaystyle{\implies\sf\:2^{(\:2x\:-\:3\:)}\:=\:2^{6x}}$

Bases are equal, so by comparing the powers, we get,

$\displaystyle{\implies\sf\:2x\:-\:3\:=\:6x}$

$\displaystyle{\implies\sf\:-\:3\:=\:6x\:-\:2x}$

$\displaystyle{\implies\sf\:4x\:=\:-\:3}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:-\:\dfrac{3}{4}\:}}}}$