Question

can anyone explain how to do this please?

Answer 1

its just an application of your basic log properties.

what are your log properties?

Answer 2

product, quotient, and power?

Answer 3

those seem good. can you give some general examples?

Answer 4

for quotient it could be something like

Answer 5

ok, im satisfied you know the rules

lets apply them

log(x) + log(x+5)

combine them back into a product, what do we get?

Answer 6

recall log(ab) = log(a) + log(b)

Answer 7

x^2+5x? :/

Answer 8

yep

so log(x^2+5x) = 2

lets undo the log, base both sides by 6 in this case

x^2 +5x = 6^2

now all we have is some ordinary basic boring timey whimey quadratic stuff ...

Answer 9

how do you solve a quadratic?

Answer 10

you set it to zero?

Answer 11

so you move the 6^2 or 36 to the left?

Answer 12

so far so good, keep going :)

Answer 13

the most common solution is a result of the quadratic formula. which is just a result a generalized completing of the square

Answer 14

if factoring is more your speed, that works too

Answer 15

-9 and 4???

Answer 16

yep

now we need to determine if any of these are valid in our setup

Answer 17

what do we not want in logs?

Answer 18

negatives

Answer 19

then log(-9) is no good

and log(4+5) seems fine so whats our choice for x?

Answer 20

4!!

Answer 21

then we have come to the finale :) x = 4 is good for me

Answer 22

omg thank you so much!!! I actually understood haha

Answer 23

your welcome :) good luck