What does the letter X equal?

Question

log x + log 3 = log 18

x = 

I got 6 and 6.0001 but it's incorrect.

Answer 1

To solve problems involving logarithms you usually need to use properties of exponential and logarithmic functions.

For this type of problem, the two following properties are useful:

1) log(a)+log(b) = log(ab) (when all logs are of the same base)

2) log(a) = log(b) means a = b (again when the logs are of same base).

Then by property 1),

log(18) = log(x) + log(3) = log(3x)

so by property 2),

log(18) = log(3x) implies 3x =18.

Solving for x (by dividing by 3) we obtain

x = 6.

Notice that in order to use the above properties you must know that the logs are using the same base, otherwise we cannot use those properties.

Answer 2

6 should be correct because of the rules of logarithms.

log x + log 3 = log (3x)

log (3x) = log 18

3x = 18

x = 6.