Pregunta
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Solve for
i
if
iii
iv

Ask by Knight Cox. in South Africa
Jan 23,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

The solutions are:

Solución

Solve the equation .
Solve the equation by following steps:
  • step0: Solve for :
  • step1: Subtract the terms:
  • step2: Divide both sides:
  • step3: Divide the numbers:
  • step4: Set the exponents equal:
  • step5: Move the constant to the right side:
  • step6: Add the numbers:

    Solve the equation .
    Solve the equation by following steps:
  • step0: Solve for :
  • step1: Add the terms:
  • step2: Divide both sides:
  • step3: Divide the numbers:
  • step4: Rewrite in exponential form:
  • step5: Set the exponents equal:

    Solve the equation .
    Solve the equation by following steps:
  • step0: Solve for :
  • step1: Simplify:
  • step2: Divide both sides:
  • step3: Divide the numbers:
  • step4: Rewrite in exponential form:
  • step5: Set the exponents equal:

    Solve the equation .
    Solve the equation by following steps:
  • step0: Solve for :
  • step1: Add the terms:
  • step2: Divide both sides:
  • step3: Divide the numbers:
  • step4: Rewrite in exponential form:
  • step5: Set the exponents equal:

    Solve the equation .
    Solve the equation by following steps:
  • step0: Solve for :
  • step1: Move the expression to the left side:
  • step2: Rewrite the expression:
  • step3: Rewrite the expression:
  • step4: Use substitution:
  • step5: Rewrite in standard form:
  • step6: Solve using the quadratic formula:
  • step7: Simplify the expression:
  • step8: Simplify the expression:
  • step9: Separate into possible cases:
  • step10: Rewrite the fraction:
  • step11: Substitute back:
  • step12: Solve the equation for
  • step13: Find the union:

    The solutions to the given equations are:

Respondido por UpStudy AI y revisado por un tutor profesional

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Bonus Knowledge

To solve for in each equation step-by-step:
i. Start with . Rewrite it as , so . Thus, . Therefore, since .
ii. For , rewrite as . Combine like terms: gives . Thus, .
iii. The equation simplifies to . Dividing by 3: leads to since .
iv. In , we rewrite it as . Dividing by 2 gives , which means since .
v. For , note that . This rewrites the equation to . Let ; then, the equation becomes . Rearranging gives . Using the quadratic formula results in two possible values for . This can be further simplified for finding .
So the values of are:
i.
ii.
iii.
iv.
v. Solve that quadratic for values of .
Happy solving!

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