Question

If log X base16+logXbase4+logXbase2 equal to 14 then X

Answer 1

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Question :-

$\log _{16}\left(x\right)+\log _4\left(x\right)+\log _2\left(x\right)=14\ \ :\mathrm{Find\ x}$

Answer :-

$\mathrm{x=256}$

Step-By-Step Explanation :-

$\log _{16}\left(x\right)+\log _4\left(x\right)+\log _2\left(x\right)=14$  ------------------------------------ eq ( 1 )

• $\log _{16}\left(x\right) = \frac{1}{4} \log _2\left(x\right)$

• $\log _4\left(x\right)=\frac{1}{2} \log _2\left(x\right)$

$\bigstar\ \bf{Substituting\ Simplified\ Values\ in\ equation-1}\ \bigstar$

⇒ $\frac{1}{4} \log _2\left(x\right) + \frac{1}{2} \log _2\left(x\right)\ +\ } \log _2\left(x\right)=14$

$\bigstar\ \bf{Taking\ \log _2\left(x\right)\ common}\ \bigstar$

⇒ $(\frac{1}{4} +\frac{1}2} +1 )\log _2\left(x\right)=14$

⇒ $\frac{7}{4} \log _2\left(x\right)=14$

$\bigstar\ \bf{Shifting\ \frac{7}{4}\ towards\ R.H.S }\ \bigstar$

⇒ $} \log _2\left(x\right)=14\ \times \frac{4}{7}$

⇒ $\log _2\left(x\right)=2 \times 4$

⇒ $\log _2\left(x\right)=8$

⇒ $x\right)=2^{8}$

$x = 256$

                $\huge{\boxed{\boxed{\boxed{\mathrm{\therefore\:Answer\:\dashrightarrow\:\bf{x=256}}}}}}$

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Hope It Helps You Dear ! :D     ^_^

By Abhiram5566

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Answer 2

Answer:

hi

Explanation:

thanks for askign question

i dont know answer