Logarithms-26

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Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.

log₈ (x + 4) + log₈ (x + 2) = log₈ 48

Solution:

log₈ (x + 4) + log₈ (x + 2) = log₈ 48

or, log₈ [(x + 4)(x + 2)]=log₈ 48

or, x²+6x+8=48

or, x²+6x-40=0

or, x²+10x-4x-40=0

or, x(x+10)-4(x+10)=0

or, (x+10)(x-4)=0

Either , x+10=0 or, x= -10 .

Or, x-4=0 or, x=4 .