Question

log5(x)-log5(x-2)=3 how do you solve this?

Answer 1

do you know the log properties ??

Answer 2

im not too sure what they are, my teacher isnt very good at explaining

Answer 3

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

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

Answer 4

look at your question and log properties
which one you should apply first ??

Answer 5

the quotient rule?

Answer 6

yes right bec there is negative sign
go ahead and apply that :-)

Answer 7

log5(x) - log5(x-2) = log5(x/x-2)
Then : log5(x/x-2) = 3
which will be :
\[\frac{ x }{ x-2 } = 5^{3}\]

by simplifying the above equation you will get : x = 125x - 250
then : x = 250/124
Let me know if you got it :)

Answer 8

ok so i got it up to log5(x-2/x)=3 but i dont know what to do from there

Answer 9

nope remember first number should be at the top