Question

Solve the equation
log base 5 (4x+1)=log base 5 (2x+7)

Answer 1

log base 5 (4x+1)=log base 5 (2x+7)

4x+1 = 2x + 7

4x+1-2x = 7

4x - 2x = 7 - 1

keep going to solve for x

Answer 2

make sure you check any and all potential answers you get

Answer 3

are both x the same?

Answer 4

what do you mean

Answer 5

am i going to get 1 answer or two?

Answer 6

just one potential answer, but you should always check any and all potential answers you get

Answer 7

im lost my you help?

Answer 8

4x - 2x = 7 - 1

2x = 6

x = ???

Answer 9

the phrase combine like terms may help you understand what @jim_thompson5910 is saying

Answer 10

x=3

Answer 11

yes

Answer 12

whats my next step?

Answer 13

that's it

Answer 14

okay may you explian this to me

Answer 15

well you have the answer, so you're done, but you should always check your answers

Answer 16

this is given

log base 5 (4x+1)=log base 5 (2x+7)

Answer 17

the logs are the same base, so the stuff inside the logs must be equal

4x+1 = 2x+7

Answer 18

from here, we solve this as any other linear equation: get x all by itself on one side

Answer 19

oh so you combined the like terms

Answer 20

yes something like 2x and 5x are like terms

if you add them, you get 2x+5x = 7x

Answer 21

lol yess i get it now

Answer 22

"log base 5 (4x+1)=log base 5 (2x+7)"

You check your answer for at least two reasons:

1) Errors can occur.
2) Fundamental things can go wrong.

In this case, these two things are NOT QUITE equivalent.

log base 5 (4x+1)=log base 5 (2x+7)

and

4x+1 = 2x+7

This is a Domain problem.

You can try any value you like in 4x+1 or 2x+7, but this is not so of the logarithms of those values. Try x = -1.

4(-1) + 1 = -4 + 1 = -3 -- Nothing wrong with that.
log(-3) -- That's no good!