sove for x.    log 3 (x) + log 3 (2) = 2

Expert Answers
hala718 eNotes educator| Certified Educator

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

We know that:

log a + log b = log a*b

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

==> log 3 (2x) = 2

==> 2x = 3^2

==> 2x = 9

==> x= 9/2 = 4.5

Then the answer is:

x= 4.5

giorgiana1976 | Student

Let's try the following method. We'll subtract log 3 (2) both sides:

log 3 (x) = 2 - log 3 (2)

We'll re-write 2 as:

2 = 2*1

We'll substitute the value 1 by log 3 (3).

2 = 2*log 3 (3)

We'll use the power property of the logarithms:

2 = log 3 (3)^2

We'll re-write the equation:

log 3 (x) = log 3 (3)^2 - log 3 (2)

Because the bases are matching, we'll transform the difference of logarithms from the right side, into a quotient:

log 3 (x) = log 3 (9/2)

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

x = 9/2

x = 4.5

Since the value of x is positive, the solution of the equation is valid.

william1941 | Student

Here we use the relation log A + log B= log A*B

( log refers to logarithm to the base 3)

log x + log 2 = 2

=> log (2*x) = 2

Raise the left and right hand sides to the power of 3.

3^ log (2*x) = 3^2

=> 2x = 9

=> x= 9/2

Therefore x = 9/2

neela | Student

To solve for x. log3(x)+log4(2) = 2

We rewrite the right side of the equation 2  as log base3. So 2= log3 (3^2). So the equation becomes:

log3(x)+log3(2) = log3 (3^2).

log3 (x*2) = log3 (9) , as loga+logb = log(ab).

Take antilog.

2x = 9.

x = 9/2.