Question

4 power x equal to eight power 2 how to do the sum explain​

Answer 1

Answer:

x

$x {}^{4} = 8 {}^{2} \\ \\ x {}^{4} = 16 \\ \\ x {}^{4} = 2$

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Answer 2

Answer:

$4 ^ x = 8 ^ 2 \quad : \quad x = 3$

Step-by-step explanation:

$4 ^ x = 8 ^ 2$

$\gray{ \mathrm{ C o n v e r t \: } 4 ^ x \mathrm{ \: t o \: b a s e \: } 2 }$

$\gray{ 4 ^ x = \left( 2 ^ 2 \right) ^ x }$

$\left( 2 ^ 2 \right) ^ x = 8 ^ 2$

$\gray{ \mathrm{ C o n v e r t \: } 8 ^ 2 \mathrm{ \: t o \: b a s e \: } 2 }$

$\gray{ 8 ^ 2 = \left( 2 ^ 3 \right) ^ 2 }$

$\left(2^2\right)^x=\left(2^3\right)^2$

$\gray{\mathrm{ A p p l y \: e x p o n e n t \: r u l e } : \quad \left( a ^ b \right) ^ c = a ^ { b c }}$

$\gray{ \left( 2 ^ 2 \right) ^ x = 2 ^ { 2 x } , \: \space \left( 2 ^ 3 \right) ^ 2 = 2 ^ { 3 \cdot \: 2 }}$

$2^{2x}=2^{3\cdot \:2}$

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

$2x=3\cdot \:2$

$\gray{\mathrm{Simplify}}$

$2x=6$

$\mathrm{Solve\:}\:2x=6$

$2x=6$

$\gray{\mathrm{Divide\:both\:sides\:by\:}2}$

$\dfrac{2x}{2}=\dfrac{6}{2}$

$\gray{\mathrm{Simplify}}$

$x=3$