00:01
Okay, so this one says, for what value of x is 8 to the 2x minus 4 equal to 16 to the x? so the key to this kind of a question is to make sure that we have it in the same base.
00:11
Currently, we have one base as 8 and one base as 16, so they're not the same base.
00:16
Well, we can make it into the same base because we know that these both can be written as a base of 2.
00:21
So instead of 8, we're going to call that 2 to the 3rd power, because 2 to 3rd power is 2 times 2, which is 8.
00:30
And again with the 16, we're going to represent that as 2 to the 4th, because 2 times 2 times 2 times 2 times 2 is equal to 16.
00:37
So then from here, we can go ahead and rewrite this by substituting this 2 to the 3rd in for the 8.
00:44
Then we can say 2 to the 3rd to the 2x minus 4 power is equal to 2 to the 4 to the x power.
00:51
So we just substituted this in right here.
00:55
So then we're going to expand this, and we know that if we have an exponent raised to the exponent, power, we know that we just have to multiply the numbers.
01:04
Then we can say 2 to the 6x minus 12...