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3 years ago

Solution set answer...............

Mathematics

1 answer:

dmitriy555 [2]3 years ago

3 0

Answer:

x= 3/2

Step-by-step explanation:

log3(x) + log3(2x-1) =1

We know that log a+log b = log ab

log3((x)(2x-1)) = 1

Raise each side to the base 3

3^log3((x)(2x-1)) = 3^1

x*(2x-1) = 3^1

Distribute

2x^2 -x = 3

Subtract 3 from each side

2x^2 -x-3 = 3-3

2x^2 -x-3 = 0

Factor

(2x-3) (x+1) =0

Using the zero product property

2x-3 =0 x+1 =0

2x=3 x=-1

x = 3/2 x =-1

But we cannot take logs of negatives ( as we see when we put it back in the original equation)

so x=-1 is an extraneous solution

x= 3/2

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