𝑙𝑜𝑔2𝑥+𝑙𝑜𝑔2(𝑥+2)=𝑙𝑜𝑔2(𝑥+6)?

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I need some help with solving this equation. Thanks

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Answer 1 · 2018-03-05T15:32:54

#x=3#

I think you mean #log_2x+log_2(x+2)=log_2(x+6)#

According to the laws of logarithms, #loga+logb=logab#. So here:

#log_2(x(x+2))=log_2(x+6)#

As the bases are equal, we can write the above as:

#x^2+2x=x+6#

#x^2-x-6=0#

#x^2+2x-3x-6=0#

#x(x+2)-3(x+2)=0#

#(x+2)(x-3)=0#

So #x=-2# or #x=3#

But, remember that if #f(x)=logx#, and #x<=0#, #f(x)# is undefined. So #-2# is not in the solution set.

So we can say that #x=3#