Question

4 power x is equal to 8 power 2 how to do the same explain​

Answer 1

Answer:

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

Step-by-step explanation:

$4^x=8^2$

$\gray{\mathrm{Convert\:}4^x\mathrm{\:to\:base\:}2}$

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

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

$\gray{\mathrm{Convert\:}8^2\mathrm{\:to\:base\:}2}$

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

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

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}}$

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

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

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

$2x=3\cdot \:2$

$\gray{\mathrm{Simplify}}$

$2x=6$

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

$2x=6$

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

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

$\gray{\mathrm{Simplify}}$

$x=3$

Answer 2

Answer:

4^x=8^2\quad :\quad x=34

x

=8

2

:x=3

Step-by-step explanation:

4^x=8^24

x

=8

2

\gray{\mathrm{Convert\:}4^x\mathrm{\:to\:base\:}2}Convert4

x

tobase2

\gray{4^x=(2^2)^x}4

x

=(2

2

)

x

(2^2)^x=8^2(2

2

)

x

=8

2

\gray{\mathrm{Convert\:}8^2\mathrm{\:to\:base\:}2}Convert8

2

tobase2

\gray{8^2=(2^3)^2}8

2

=(2

3

)

2

(2^2)^x=(2^3)^2(2

2

)

x

=(2

3

)

2

\gray{\mathrm{Apply\:exponent\:rule}:\quad (a^b)^c=a^{bc}}Applyexponentrule:(a

b

)

c

=a

bc

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

2

)

x

=2

2x

, (2

3

)

2

=2

3⋅2

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

2x

=2

3⋅2

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

f(x)

=a

g(x)

,thenf(x)=g(x)

2x=3\cdot \:22x=3⋅2

\gray{\mathrm{Simplify}}Simplify

2x=62x=6

\gray{\mathrm{Solve\:}\:2x=6}Solve2x=6

2x=62x=6

\gray{\mathrm{Divide\:both\:sides\:by\:}2}Dividebothsidesby2

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

2

2x

=

2

6

\gray{\mathrm{Simplify}}Simplify

x=3x=3