Chapter 5: Q.80 (page 316)

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places :
$\log_{2} (x^{\log_{2} (x)}) = 4$

Short Answer

Expert verified

The value of x satisfying the equation is $x = 4 a n d x = 0.25$

Step by step solution

Given information

We are given an equation $\log_{2} (x^{\log_{2} (x)}) = 4$

Simplify

We get,

$\log_{2} (x^{\log_{2} (x)}) = 4 \log_{2} (x) \log_{2} (x) = 4 {(\log_{2} (x))}^{2} = 4 \log_{2} (x) = \pm 2$

Solve for x

We get,

$\log_{2} (x) = \pm 2$

We use the formula $y = \log_{a} (x) \Leftrightarrow x = a^{y}$

We get

$\log_{2} (x) = 2 x = 2^{2} x = 4 A n d \log_{2} (x) = - 2 x = 2^{- 2} x = 0.25$

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places :
$\log_{2} (x^{\log_{2} (x)}) = 4$

Short Answer

Step by step solution

Given information

Simplify

Solve for x

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places :log2xlog2x=4

Short Answer

Step by step solution

Given information

Simplify

Solve for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Statistics

Applied Mathematics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places :
$\log_{2} (x^{\log_{2} (x)}) = 4$