Logarithms Practice Test 1

Question : 3 of 40

Marks: +1, -0

The positive solution of the equation

\log_{x+3}(x^2+6x+9)+\log_{5x+2} (6x^2-6x)=\log_{2x-1}(8x^3-12x^2+6x-1)

Solution:

\log_{x+3}(x^2+6x+9)+\log_{5x+2} (6x^2-6x)=\log_{2x-1}(8x^3-12x^2+6x-1)

⇒\log_{x+3}(x+3)^2+\log_{5x+2} (6x^2-6x)=\log_{2x-1}(2x-1)^3

⇒2\log_{x+3}(x+3) +\log_{5x+2} (6x^2-6x)=3\log_{2x-1}(2x-1)

⇒ \log_{5x+2} (6x^2-6x)=3-2=1

⇒5x+2=6x^2-6x

⇒6x^2-11x-2=0

⇒(6x+1)(x-2)=0

⇒x=-1/6\or2

So, positive solution is x = 2

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