Solve for x log 3 (2x+3) -1 = 0.

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

Move 1 to the right side:

==> log 3 (2x+3) = 1

We know that log 3 (3) = 1

==> log 3 (2x + 3) = log 3 (3)

We know that:

if log a = log b ==> a = b

==> 2x + 3 = 3

Subtract 3:

==> 2x = 0

==> x= 0

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll start by imposing the constraints of existance of logarithm function.

2x+3>0

We'll add -3 both sides:

2x>-3

We'll divide by 2:

x>-3/2

So, for the logarithms to exist, the values of x have to belong to the interval (-3/2, +inf.)

We'll shift the free term to the right side:

 log 3 (2x+3) = 1

We'll create matching bases to the right side.

 log 3 (2x+3) =  log 3 (3)

Now, because the bases are matching, we'll apply the one to one property:

2x+3 = 3

We'll eliminate like terms:

2x = 3-3

2x = 0

We'll divide by 2:

x = 0 > -3/2

Since the value for x belongs to the interval (-3/2,+inf.), the solution is valid.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

log(2x+3)-1 = 0. To solve for x.

Solution:

 log3 (2x+3) -1 = 0. Add 1.

 log3 (2x+3) = 1.

log3 (2x+3) = log 3 (3). Take antilog:

(2x+3) = 3

2x = 0

x = 0

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