Question

Solve the logarithmic equation:

_4 means log base 4 (for clarification)

(a) log_4 (2x-18) - log_4 (x-25) = 1

(b) log_4 (x-18) + log_4 (x-3) = 2

Answer 1

ln(a) + ln(b) = ln(ab)

ln(a) - ln(b) = ln(a/b)

Answer 2

Hmm... How did you change it to ln instead of log?

Answer 3

You don't have to change it. ln is log_e. It works with all logarithm; bases have to be same, though.

Answer 4

In your problem, bases are same, so use these properties.

Answer 5

So log_4(2x-18)(x-25)?

wouldn't that factor out all crazy and not equal 1?

Answer 6

oh I got messed up. that would be... log_4 (2x-18)/log_4 (x-25) = 1
Then what I drop the log_4 since they cancel out?

Answer 7

log_4 (2x-18)/(x-25) = 1

It looks ugly but it will look nicer when you convert this equation into exponent form.

Answer 8

Can you do it?

Answer 9

no you lost me. I was absent that day and didn't pick up any of this. I know it's from Algebra but that has been a very long time ago.

Answer 10

BASE^EXPONENT = ANSWER

log_BASE ANSWER = EXPONENT

Answer 11

For explain, \(\large log_5 7x^2 = 4 \Rightarrow 5^4 = 7x^2\).

Still lost?

Answer 12

Yea lost. I am trying to look up other references cause I am completely confused.

Answer 13

This may help you: http://www.youtube.com/watch?v=yLaJydYp4BQ

Answer 14

log_4 (2x-18) - log_4 (x-25) = 1

log_4 [ (2x-18)/(x-25) ] = 1

(2x-18)/(x-25) = 4^1

(2x-18)/(x-25) = 4

2x-18 = 4(x-25)

I'll let you take it from here. Remember to check any and all possible answers

Answer 15

still lost.

Answer 16

Did you watch the video from the given link above here?

Answer 17

yea

Answer 18

Still lost? Try another video on suggestions list.