Solve the logarithmic equation: ln(4x-3)+ln(4x+3)-ln 3=8.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation ln(4x-3) + ln(4x+3) - ln 3 = 8 has to be solved

ln(4x-3) + ln(4x+3) - ln 3 = 8

Use the property of logarithms ln a + ln b = ln (a*b) and ln a - ln b = ln(a/b)

=> `ln(((4x - 3)(4x + 3))/3) = 8`

=> `ln((16x^2 - 9)/3) = 8`

=> `(16x^2 - 9)/3 = e^8`

=> `16x^2 = 3*e^8 + 9`

=> `x^2 = (3e^8 + 9)/16`

=> `x = sqrt(3e^8+9)/4`

The other root of the equation is not considered as the logarithm of negative numbers is not defined.

The solution of the given equation is `x = sqrt(3*e^8+9)/4`

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