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Question

Solve for x :

6x+4x=9x


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Solution

4x+6x=9x

On dividing both sides by 4x we get

1+64x=94x

1+32x=322x

322x-32x-1=0

32x2-32x-1=0

Let us assume that 32x=y the equation becomes,

y2-y-1=0...........................(i)

Using quadratic formula i.e. y=-b±b2-4ac2a

Comparing equation (i) with the general form of the quadratic equation we get a=1,b=-1,c=-1

y=1±-12-4×1×-12×1

y=1±1+42

y=1±52

32x=1±52(taking log both sides we get)

xlog32=log1±52(as log of 2 is not defined)

x=log1±52log32


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