Question

find x
leg(x+1) + log(x-6) = 2 log 8​

Answer 1

Answer:

Logarithm laws:-

log_{m}(a) + log_{m}(b) = log_{m}(ab) xlog_{m}(a) = log_{m}( {a}^{x} )

log (x + 1) + log (x - 6) = log ( {8}^{2}

log{(x + 1)(x - 6)} = log( {8}^{2} )

cancelling log from both sides

(x + 1)(x - 6) = {8}^{2}

{x}^{2} + x - 6x - 6 = 64

{x}^{2} - 5x - 6 - 64 = 0

{x}^{2} - 5x - 70 = 0

{x}^{2} + 2x - 7x - 70 = 0

x(x - 2) - 7(x + 10) = 0

(x - 2)(x - 7)(x + 10) = 0

x = 2 or x = 7 or x = -10