algebra

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solve the logarithm
log_2 (x -1)- log_2(5x +1) = -3

I got -3, is this correct???????

  • algebra -

    assuming base 2 for ease of reading,

    log(x-1) - log(5x+1) = -3
    log[(x-1)/(5x+1)] = -3
    (x-1)/(5x+1) = 2^-3 = 1/8
    8(x-1) = 5x+1
    8x - 8 = 5x + 1
    3x = 9
    x = 3

    log 2 - log 16 = 1 - 4 = -3

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