Math

Find the exact solution, using common logarithms, and a two-decimal-place approximation of each solution.

log(7x + 4) = 2 + log(2x − 3)

Solve the equation.

log(x^3) = (log x)^2

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  1. log(7x + 4) = 2 + log(2x − 3)
    log(7x + 4) - log(2x − 3) = 2
    log( (7x+4)/(2x-3) ) = 2
    (7x+4)/(2x-3) = 10^2 = 100
    200x - 300 = 7x+4
    193x = 304
    x = 304/193 or appr 1.575

    for the 2nd

    log x^3 = log x^2
    x^3 = x^2
    x^3 - x^2 = 0
    x^2(x-1) = 0
    x = 0 or x = 1

    but from log(2x-3) , 2x-3 > 0
    2x > 3
    x > 3/2

    so there is not solution.

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