Question

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

Answer 1

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

Answer:

${2}^{2x + 2} = {4}^{2x - 1} \\ {2}^{2x + 2} = {2}^{2(2x - 1)} \\ {2}^{2x + 2} = {2}^{4x - 2} \\ equating \: powers \: from \: both \\ \: sides \: we \: find \: \\ 2x + 2 = 4x - 2 \\ 2 + 2 = 4x - 2x \\ 4 = 2x \\ x = \frac{4}{2} \\ x = 2$