How can logarithms help solve an equation involving trigonometric functions?

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    Logarithms Trigonometry
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Discussion Overview

The discussion revolves around solving an equation involving trigonometric functions and logarithms, specifically the equation 4^{sinx} = \sqrt[cosx]{2}. Participants explore the application of logarithmic properties and trigonometric identities to simplify and solve the equation.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant expresses an initial approach using logarithms, leading to the equation sinx * log(4) = (1/cosx) * log(2).
  • Another participant suggests applying the change of base rule to simplify log(2)/log(4) and encourages the use of trigonometric formulas for further simplification.
  • A later post reiterates the initial approach and asks for clarification on the value of log(2)/log(4).
  • One participant concludes by stating they have solved the problem, but does not provide details on the solution.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants provide different levels of engagement with the problem, and the final solution is not shared in detail.

Contextual Notes

Some assumptions regarding the properties of logarithms and trigonometric identities are not explicitly stated, and the steps leading to the final solution remain unresolved.

Who May Find This Useful

Individuals interested in the interplay between logarithmic functions and trigonometric equations, particularly in a mathematical or problem-solving context.

Petkovsky
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4[tex]^{sinx}[/tex] = [tex]\sqrt[cosx]{2}[/tex]

I use logarithmic and i get :

sinx * log(4) = (1/cosx) * log(2)

sinx*cosx = log(2)/log(4)


what should i do next?
 
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What is log(2)/log(4)? Try applying a change of base rule. Afterward, see if you can use any of your trigonometric formulas to simplify.
 
Petkovsky said:
4[tex]^{sinx}[/tex] = [tex]\sqrt[cosx]{2}[/tex]

I use logarithmic and i get :

sinx * log(4) = (1/cosx) * log(2)

sinx*cosx = log(2)/log(4)


what should i do next?

What is log(2)/log(4) ?
 
Thank you, i solved it
 

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