00:01
In this problem, we have been asked to determine the value of x that satisfies the given equation.
00:06
Now the equation that we have been given is log base 3 of x plus 12 plus log base 3 of x plus 6.
00:17
This is equal to 3.
00:19
So on the left hand side, first of all, let us use the product rule of logarithms.
00:24
Using that, the left hand side will become log base 3 of x plus 12 times x plus 6.
00:30
So this is equal to 3.
00:32
So we are going to obtain that x plus 12 times x plus 6.
00:37
This is equal to 3 to the power of 3.
00:41
3 raised to the power of 3.
00:44
So on the left hand side, we have x squared plus 6x plus 12x plus 12 times 6.
00:50
That is 72.
00:51
This is equal to 3 cubed.
00:53
That is 27.
00:55
So we have x squared plus 6x plus 12x.
00:57
That is 18x.
00:59
We have 72 minus 27.
01:01
This is 0.
01:01
So x squared plus 18x plus 72 minus 27.
01:07
That is equal to 45.
01:10
So this is equal to 0.
01:14
So what we are going to do is we are going to rewrite 18x as 3x plus 15x.
01:20
And from the first two terms, we can factor out x to get x times x plus 3...