Question

solve 2 ki power X equal to 128 ki power 1/7 into root 2 ki power 4​

Answer 1

Answer:

x = 3

Step-by-step explanation:

Given :

$\large \text{ 2^x=128^{\frac{1}{7}}\times(\sqrt{2})^4 }$

We have to find value of x.

Rewrite  128 as $2^7$  and  $\large \text{ \sqrt{2} \ as \ 2^{\frac{1}{2}} }$

$\large \text{ 2^x=2^{\frac{7}{7}}\times(2^{\frac{4}{2}}) }\\\\\\\large 2^x=2\times2^2$

We know that when base is base then power added.

$\large 2^x=2\times2^2\\\\\\\large 2^x=2^{1+2}$

Comparing both side we get

x = 1 + 2

x = 3

Verification:

putting values of x = 3 here

$\large 2^x=2\times2^2\\\\\\\large 2^3=2\times4\\\\\\\large 8=8$

L.H.S. = R.H.S.

Hence verified.

Answer 2

Answer:

$2^x=128^{\dfrac{1}{7}}\left(\sqrt{2}\right)^4\quad :\quad x=3$

Step-by-step explanation:

$2^x=128^{\dfrac{1}{7}}\left(\sqrt{2}\right)^4$

$\gray{\mathrm{Convert\:}128^{\dfrac{1}{7}}\left(\sqrt{2}\right)^4\mathrm{\:to\:base\:}2}$

$\gray{128^{\dfrac{1}{7}}\left(\sqrt{2}\right)^4=2^3}$

$2^x=2^3$

$\gray{\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)}$

$x=3$