Question

Solve 3 log6 2 + 2 log6 3 − log6 x = 2.

x = 2
x = 6
x = 15
x = 36

Answer 1

First thing you should do is re write 2 in terms of log with a base 6

So doing that .... log (base 6) 36 is the same thing as 2.

Now you need to re write the reset of the problem using the properties of logs

log (base 6) 2^3 + log (base 6) 3^2 - log (base 6) x = log (base 6) 36

Since they all have the same base you can now just drop the log and solve for x

(8)(9)/x = 36

x = 2

Answer 2

1st Option is correct.

Explanation:

Given:

`3\,log_6\,2+2\,log_6\,3-log_6\,x=2`

To find: Value of x.

Results we use,

`a\,log\,b=log\,b^a\:\:,\:\:log\,a+log\,b=log\,ab\:,\:log\,a-log\,b=log\,(a)/(b)`

`log_a\,x=y\implies x=x^y`

Consider,

`3\,log_6\,2+2\,log_6\,3-log_6\,x=2`

`log_6\,2^3+log_6\,3^2-log_6\,x=2`

`log_6\,((8*9)/(x))=2`

`(72)/(x)=6^2`

`x=(72)/(36)`

x = 2

Therefore, 1st Option is correct.