How to Solve a Complex Algebraic Equation with Logs and Square Roots?

  • Context: High School 
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SUMMARY

The discussion focuses on solving the algebraic equation 2x = 16 - (3/4) * sqrt(2). Participants demonstrate two methods to find the value of x, ultimately concluding that x = -2.5. The first method involves logarithmic manipulation, while the second method utilizes base conversion of 16 to base 2. Both approaches confirm the same result, showcasing the versatility of mathematical techniques in solving equations.

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  • Understanding of algebraic equations
  • Knowledge of logarithmic functions
  • Familiarity with square roots and their properties
  • Ability to convert numbers between different bases
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  • Study logarithmic properties and their applications in algebra
  • Learn about base conversions in exponential equations
  • Explore advanced algebraic techniques for solving equations
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Students, educators, and anyone interested in enhancing their algebra skills, particularly in solving complex equations involving logarithms and square roots.

Matrix
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Hi, I am having trouble finding x for the following exquation:
2x=16-3/4 * sqrt(2)

Any help on solving it would be much apprecitated.
 
Last edited:
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why don't you use logs.

2^x = 16^(-3/4) * sqrt(2)

x*ln(2) = ln(16^(-3/4) * sqrt(2) )

x = ln(16^(-3/4) * sqrt(2) ) / ln(2)
 
reduce it further to:

x = -2.5
 
jcsd, your i see you changed your reduction. The previous one was obviously wrong.
 
Is it possible to find x not using logs?
 
Duardo: No, it was perfectly correct.
 
Originally posted by Matrix
Is it possible to find x not using logs?

yes.

you can convert 16 to a base 2

16^(-3/4) = (2^4)^(-3/4) = 2^(-3)

therefore

2^x = 2^(-3) * 2^(1/2)

2^x = 2^(-5/2)

x = -2.5
 
This is probably off topic, but don't you just love logs?
 

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