Question

There are two solutions to the equation \log(30 x) + \log(x-1) = 1log(30x)+log(x−1)=1. Find the larger of the two solutions.

Answer 1

log 30x + log (x-1) = 1
there are two samw equations so why ?

Answer 2

same - equations - sorry

Answer 3

do you know this property of logarithms ?

log a + log b = log a*b

Answer 4

can using this in case of your exercise ?

Answer 5

it just got repeated
sorry.

Answer 6

ok np

but can using this formula in case of your exercise ?

Answer 7

a=30x and b=(x-1)

Answer 8

u can use anything to solve it but yeah iam familiar with it

Answer 9

but what im confused abut is the 2 solutions that they are reffering to

Answer 10

using this formula you get

log 30x +log (x-1) =1
log [30x(x-1)] = 1
log (30x^2 -30x) =1

do you know how many is the base of this logarithm noted by log ?

Answer 11

Loser how many is the base of this log. just bc. i ve learned it 2 by 35 years ago here in Europe and here in OS have wrote me that is 10 ?

Answer 12

ok- ty

Answer 13

so in this case we can rewriting the 1 like log 10

Answer 14

and will get this equation

log (30x^2 -30x) =1

log (30x^2 -30x) = log 10

30x^2 -30x = 10 do you can continue it now ?

Answer 15

subtract from both sides 10 and will get

30x^2 -30x -10 = 0 can you solving this quadratic ?

Answer 16

factorize out the 10 and will get

10(3x^2 -3x -1) = 0 divide both sides by 10 and will get

3x^2 -3x -1 = 0 can you solving it now for x ?

Answer 17

do you know formula of discriminant ?

Answer 18

please collaborate

Answer 19

i was trying to solve
the last equation you wrote.
sorry

Answer 20

yeah i do

Answer 21

3x^2 -3x -1 = 0 so can you solving this quadratic ?

Answer 22

let me solve it and confirm wiht u

Answer 23

ok. but please write here your work

Answer 24

discriminant D = ?

Answer 25

step by step please

Answer 26

ok i just solved it using the formula b+/= ....

Answer 27

and i got 2 values for x
x=1.26
x= -0.263

Answer 28

i dont know if thats right or wrong

Answer 29

D = b^2 -4ac is the formula of discriminant

Answer 30

3x^2 -3x -1 = 0

how many you have got the value for discriminant ?

Answer 31

21

Answer 32

D = 9 +12 = 21 yes is right

so than x_1,2 = ?

Answer 33

im confused
what are using d for

Answer 34

D is the discriminant

Answer 35

after you get the value of discriminant how you get the roots x_1,2 ?

Answer 36

idk

Answer 37

so how you ve got these two values ?

Answer 38

ok. try using this

x_1,2 = (-b +/- sqrt(D) )/2a

Answer 39

3x^2 -3x -1 = 0

b = ?

Answer 40

D = b^2 -4ac = ?

Answer 41

how you get the value of discriminant ?

Answer 42

3x^2 -3x -1 = 0

a=3
b=-3
c=-1

yes ?

Answer 43

bc. there are

ax^2 +bx +c = 0

Answer 44

so can you calculi now the x_1,2 = ?

Answer 45

x_1,2 = (-b +/- sqrt(D) )/2a

Answer 46

ok ur method is different