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Solve the equation.\newlinelog⁡(x+5)=log⁡(4x+2)\log(x+5)=\log(4x+2)

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Full solution

Q. Solve the equation.\newlinelog⁡(x+5)=log⁡(4x+2)\log(x+5)=\log(4x+2)
  1. Set Equations Equal: We have the equation log⁡(x+5)=log⁡(4x+2)\log(x+5) = \log(4x+2).\newlineSince the logarithms are equal and have the same base, their arguments must be equal.\newlineSet the arguments equal to each other: x+5=4x+2x+5 = 4x+2.
  2. Combine Like Terms: Subtract xx from both sides to get all xx terms on one side: x+5−x=4x+2−xx+5-x = 4x+2-x. This simplifies to 5=3x+25 = 3x+2.
  3. Isolate x Term: Subtract 22 from both sides to isolate the term with xx: 5−2=3x+2−25-2 = 3x+2-2. This simplifies to 3=3x3 = 3x.
  4. Solve for x: Divide both sides by 33 to solve for xx: 33=3x3\frac{3}{3} = \frac{3x}{3}. This simplifies to 1=x1 = x.

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