Math, asked by muskan2145, 11 months ago

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

Answers

Answered by Anonymous
25

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 \text{$2^x=2\times2^2$}

We know that when base is base then power added.

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

Comparing both side we get

x = 1 + 2

x = 3

Verification:

putting values of x = 3 here

\large \text{$2^x=2\times2^2$}\\\\\\\large \text{$2^3=2\times4$}\\\\\\\large \text{$8=8$}

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

Hence verified.

Answered by AbhijithPrakash
10

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

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