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Solve for x: log2(3x+3) = log2(64)

Mathematics

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Answer

613\frac{61}{3}

Step-by-step solution

3 steps

Ili kutatua mlinganyo wa logariti, tutatumia kanuni za logariti.

  1. Tumia kanuni ya logariti inayosema kwamba ikiwa log⁡bM=log⁡bN\log_b M = \log_b N, basi M=NM = N.

    log⁡2(3x+3)=log⁡264\log_2 (3x+3) = \log_2 64

    Hii inamaanisha kuwa hoja za logariti lazima ziwe sawa.

    3x+3=643x+3 = 64

  2. Ondoa 3 kutoka pande zote mbili za mlinganyo.

    3x=64−33x = 64 - 3 3x=613x = 61

  3. Gawanya pande zote mbili kwa 3 ili kupata thamani ya xx.

    x=613x = \frac{61}{3}

    The final answer is 613\frac{61}{3}.

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