answersLogoWhite

0

We can't see the parentheses, and there are at least two ways to read this.

Here are solutions for the most likely two:

--------------------------------------------------------

log(x) - 3 + log(x) - 2 = log(2x) + 24

Add 5 to each side:

log(x) + log(x) = log(2x) + 29

Subtract log(2x) from each side:

log(x) + log(x) - log(2x) = 29

Combine the logs on the left side, and massage:

log( x2/2x ) = log( x/2 ) = 29

Take the antilog of each side:

x/2 = 1029

Multiply each side by 2:

x = 2 x 1029

------------------------------------------------

log(x - 3) + log(x - 2) = log(2x + 24)

Combine logs on the left side:

log[ (x-3) (x-2) ] = log(2x + 24)

Take antilog of each side:

(x-3) (x-2) = 2x + 24

Expand the left side:

x2 - 5x +6 = 2x + 24

Subtract (2x+24) from each side:

x2 - 7x - 18 = 0

Factor:

(x - 9) (x + 2) = 0

Whence:

x = 9

x = -2

We have to discard the solution [ x = -2 ] because one term in the equation

is log(x-2).

If 'x' were -2 then we'd have log(-4) but negative numbers don't have logs.

User Avatar

Wiki User

13y ago

Still curious? Ask our experts.

Chat with our AI personalities

BlakeBlake
As your older brother, I've been where you are—maybe not exactly, but close enough.
Chat with Blake
SteveSteve
Knowledge is a journey, you know? We'll get there.
Chat with Steve
JudyJudy
Simplicity is my specialty.
Chat with Judy

Add your answer:

Earn +20 pts
Q: How do you sole X when logx-3 plus logx-2 equals log2x plus 24?
Write your answer...
Submit
Still have questions?
magnify glass
imp