2 ka power 2x+2 = 4 ka power 2x-1 find value of x

1.	2 ka power 2x+2 = 4 ka power 2x-1 find value of x
Answer» ANSWER: $2^{2x+2}=4^{2x-1}\quad :\quad x=2$ Step-by-step EXPLANATION: $2^{2x+2}=4^{2x-1}$ $\gray{\mathrm{Convert\:}4^{2x-1}\mathrm{\:to\:base\:}2}$ $\gray{4^{2x-1}=\left(2^2\right)^{2x-1}}$ $2^{2x+2}=\left(2^2\right)^{2x-1}$ $\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}}$ $\gray{\left(2^2\right)^{2x-1}=2^{2\left(2x-1\right)}}$ $2^{2x+2}=2^{2\left(2x-1\right)}$ $\gray{\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)}$ $2x+2=2\left(2x-1\right)$ $\black{\mathrm{Solve\:}\:2x+2=2\left(2x-1\right)}$ $2x+2=2\left(2x-1\right)$ $\gray{\mathrm{Expand\:}2\left(2x-1\right):\quad 4x-2}$ $2x+2=4x-2$ $\gray{\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}}$ $2x+2-2=4x-2-2$ $\gray{\mathrm{Simplify}}$ $2x=4x-4$ $\gray{\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}}$ $2x-4x=4x-4-4x$ $\gray{\mathrm{Simplify}}$ $-2x=-4$ $\gray{\mathrm{Divide\:both\:sides\:by\:}-2}$ $\dfrac{-2x}{-2}=\dfrac{-4}{-2}$ $\gray{\mathrm{Simplify}}$ $x=2$

Answer»

$2^{2x+2}=4^{2x-1}\quad :\quad x=2$