Question

Solve for x. log(x) + log(x - 3) = 1 Please explain how you got the answer.

Answer 1

familiar with log rules ?

Answer 2

No I forgot them. That's why I need help with this. Can you help me?

Answer 3

quotient rule\[\large\rm log_b y - \log_b x = \log_b \frac{ x }{ y}\]
to condense you can change subtraction to division
product rule \[\large\rm log_b x + \log_b y = \log_b( x \times y )\]
addition ----> multiplication

power rule \[\large\rm log_b x^y = y \log_b x\]

Answer 4

so there is a plus sign which rule you should apply ?

Answer 5

addition ----> multiplication

Answer 6

How do you know which number is b?

Answer 7

yep so change addition to multiplication
log is same so you can apply it

Answer 8

b is base

Answer 9

so log is same as log base 10 \[\huge\rm log = \log_{10}\]

Answer 10

So is it log(x*(x-3))?

Answer 11

Or log(x^2-3x)?

Answer 12

yep right!!

Answer 13

So what do you do with the 1?

Answer 14

now you have \[\huge\rm log (x^2 -3x) =1\]
next step
convert log to exponential form

Answer 15

How do you do that again?

Answer 16

and here is the example