00:01
Okay, so we need to solve log base 6 of 3x plus 2 is equal to 2.
00:10
We can write this as log base 6 of 3x plus 2 is equal to log base 6 of 6 squared.
00:23
Remember, if you have the same base as the base of your logarithm, it brings down the power.
00:29
So this means 3x plus 2 is equal to 6 squared.
00:34
Which is 36.
00:37
So 3x is equal to 34.
00:44
So x is equal to 34 thirds.
00:51
For part b, you have a log of 243 is equal to x plus 2.
01:09
We can rewrite this as x is equal to log base 10 let's just put that in just so remember of 243 minus 2 this is log base 10 of 243 minus log base 10 of 10 squared so we that might not be the best route to take let's rewrite 243 243 is 3 to the 5th so this is a log base 10 of 3 to the 5 minus 2 that means the 5 can come down so this is 5 log of 3 minus 2 and it's still base 10 but we usually don't write the base 10 part c 2 to the 2x minus 4 is equal to 10 so we can take the natural log of both sides.
03:18
So ln of 2 to the 2x minus 4 is equal to ln of 10.
03:27
Again, we can use the power rule.
03:29
So 2x minus 4 times ln of 2 is equal to ln of 10...