Chapter 5: Q.77 (page 316)

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{16} x + \log_{4} x + \log_{2} x = 7$

Short Answer

Expert verified

The value of x satisfying the equation is $x = 16$

Step by step solution

Given information

We are given an equation $\log_{16} x + \log_{4} x + \log_{2} x = 7$

Change the base

We get,

$\log_{16} x + \log_{4} x + \log_{2} x = 7 \frac{\log_{2} (x)}{\log_{2} (16)} + \frac{\log_{2} (x)}{\log_{2} (4)} + \log_{2} (x) = 7 \frac{\log_{2} (x)}{\log_{2} {(2)}^{4}} + \frac{\log_{2} (x)}{\log_{2} (2^{2})} + \log_{2} (x) = 7 \frac{\log_{2} (x)}{4} + \frac{\log_{2} (x)}{2} + \log_{2} (x) = 7 \log_{2} (x) + 2 \log_{2} (x) + 4 \log_{2} (x) = 28 7 \log_{2} (x) = 28 \log_{2} (x) = 4$

Solve the equation

We get,

$\log_{2} (x) = 4 U s e : y = \log_{a} (x) \Leftrightarrow x = a^{y} x = 2^{4} x = 16$

Conclusion

The value of x satisfying the equation $x = 16$ .

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{16} x + \log_{4} x + \log_{2} x = 7$

Short Answer

Step by step solution

Given information

Change the base

Solve the equation

Conclusion

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solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:log16x+log4x+log2x=7

Short Answer

Step by step solution

Given information

Change the base

Solve the equation

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Decision Maths

Geometry

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{16} x + \log_{4} x + \log_{2} x = 7$