Question

plz help explain. What is the solution of log^(2x – 3)125 = 3 ?
answers
a)x=1/3
b)x=1
c)x=7/3
d)x=4

Answer 1

Well, here this means such:
\[(2x-3)^3 = 125\]
Can you proceed from here?

Answer 2

so it means that I mulitply (2x-3) 3times?

Answer 3

Yes. Also hint: 125 is a perfect cube.

Answer 4

okay.

Answer 5

It is not 3(2x-3) it is (2x-3)(2x-3)(2x-3)

Answer 6

once I get the answer for that I can dvide?

Answer 7

Well, do you know what the perfect cube is for 125? (Do you know what a perfect cube is?)

Answer 8

5√5?

Answer 9

1*1*1 = 1
2*2*2 = 8
3*3*3 = 27
4*4*4 = 64
5*5*5 = 125

Answer 10

okay so it would be 5^3

Answer 11

Right, so you have: \[(2x-3)^3 = 5^3\]
What happens to the cubes?

Answer 12

you would put (2x-3)^5=3 don't you switch them?

Answer 13

No, this means "The base 2x-3 logarithm of 125 is 3". So it is \[(2x-3)^3 = 125\]

Answer 14

so what changed?

Answer 15

Nothing at all. You've simply rewritten 125 as 5^3
\[(2x-3)^3 = 5^3\]
So then what happens to the cubes (the ^3's)

Answer 16

okay, I understand that. umm don't they become one? srry if I'm not getting where your comming from I just started learning this.

Answer 17

Its okay. Well, to eliminate a cube, you take the cube root. Similarly to eliminate a square root, you take the square. To eliminate any exponent you can take the root of the exponent.
In simplest terms, the cubes simply go away.

Answer 18

ahh! okay gottcha. so now it becomes (2x-3)=5?

Answer 19

Thats right, and solve from there.

Answer 20

answer is 4 thank you very much.

Answer 21

That's correct. No problem.