00:02
Hi, we're given here, let's solve, it's all the following logarithmic equations.
00:07
We're given here the first one is lnx is 2 over 3.
00:12
Allen x is 2 over 3.
00:14
So allen means the base is e.
00:16
It's a natural logarithm, so base is e.
00:18
It's given as log of x with base e.
00:21
It is given as 2 over 3.
00:25
Now from here, you need to solve for x, right? so, what is to solve for x here? we're doing to do here.
00:33
We'll take e to the par.
00:34
Log x with base e and equals e to the part 2 over 3 now our property here that is given as 8 to the power log x with base e is equal to x so we get here x equal to 8 to the power 2 over 3 so we just calculate here e with the power e to the power 2 over 3 that is given as 1 .948 1 .948 run to three decimal places.
01:11
I've used the calculator here.
01:14
Now, second one is given as log of 2x minus 3 that is equal to log of 2x minus 4.
01:31
So we have property here we have log of a is equal to log of b and we have a is equal to b.
01:38
So from here we get 2x minus 3 equals 2x minus 4 right so it's all this.
01:45
We get here minus 3 equal to minus 4 that means it has no solution, right? it's going to have to be, it has no solution here.
01:57
All right.
02:00
One more thing, it's given as base two basically.
02:03
So if you take base two, again, it's been the same only.
02:05
Because you have log a, let's say with base c, is equal to log b, with base c.
02:10
Then again, you have a is equal to b.
02:12
Right.
02:13
And you've got the same answer.
02:15
Moving on to now, third one, that is given as log 4x, log 4 .6...