Question

find the value of (64)^x if 8^x+2=252+2^3x​

Answer 1

Answer:

Step-by-step explanation:

Solution

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8

x

=

2

x

64

​

⇒2

3x

=

2

x

64

​

⇒2

3x

×2

x

=2

6

⇒2

4x

=2

6

 

Since bases are same, we can equate the powers

∴4x=6

⇒x=

4

6

​

=

2

3

​

∴x=

2

3

​

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Answer 2

$\textrm{Given equation: -}$

$\rm{8^{x+2}=252+2^{3x}}$

$\;$

$\boxed{\rm{a^{m}\cdot a^{n}=a^{m+n}}}$

$\boxed{\rm{(a^{m})^{n}=a^{mn}}}$

$\;$

$\rm{8^2\cdot8^{x}=252+(2^{3})^{x}}$

$\;$

$\rm{64\cdot8^{x}=252+8^{x}}$

$\;$

$\rm{63\cdot8^{x}=252}$

$\;$

$\rm{\therefore8^{x}=4}$

$\;$

$\boxed{\rm{(a^{m})^{n}=a^{mn}}}$

$\;$

$\rm{8^{x}=(2^{3})^{x}=\underline{2^{3x}},\ 64^{x}=(2^{6})^{x}=\underline{2^{6x}}}$

$\;$

$\rm{\therefore64^{x}=(8^{x})^{2}=4^{2}=\boxed{\red\rm{16}}}$

$\;$

$\Large\textrm{Learn More}$

$\textbf{- Powers of 2}$

$\boxed{\begin{aligned}2^{1}=2\\\\2^{2}=4\\\\2^{3}=8\\\\2^{4}=16\\\\2^{5}=32\end{aligned}}$ $\boxed{\begin{aligned}2^{6}=64\\\\2^{7}=128\\\\2^{8}=256\\\\2^{9}=512\\\\2^{10}=1024\end{aligned}}$

$\;$

$\textbf{-Perfect Squares}$

$\boxed{\begin{aligned}11^{2}=121\\\\12^{2}=144\\\\13^{2}=169\\\\14^{2}=196\\\\15^{2}=225\end{aligned}}$ $\boxed{\begin{aligned}16^{2}=256\\\\17^{2}=289\\\\18^{2}=324\\\\19^{2}=381\\\\20^{2}=400\end{aligned}}$