Question

2( log 2 x − log y ) − ( log 3 + 2 log 5)

Answer 1

what are you supposed to do about it?

Answer 2

solve it

Answer 3

it is not an equation. you cant solve it.

Answer 4

cant it be simplified?

Answer 5

You want to simplify it?

Answer 6

yes

Answer 7

Is it log (2x), or log x to base 2?

Answer 8

it is log((2x/y)^2)-log 75

Answer 9

log 2x

Answer 10

not that log a - log b = log(a/b) and log a +log b = log(ab)

Answer 11

how did u get the answer dhatraditya?

Answer 12

note*

Answer 13

note also that xlog a = log a^x

Answer 14

\[2 (\log(2x)-\log y)-(\log 3+2\log 5)=2(\log {2x \over y})-\log(3*5^2)\]
=\[\log({2x \over y})^2-\log(75)=\log({4x^2 \over 75y^2})\]

Answer 15

I think this is the simplest it can be.

Answer 16

so its simplified form is log ((2x/y)^2/75))

Answer 17

What AnwarA has.

Answer 18

thank you so much

Answer 19

You're welcome!

Answer 20

how did u get the 75?

Answer 21

3*5^2=3(25)=75

Answer 22

as I explained, x log a = log a^x
so 2 log 5 = log 5^2 = log 25
log a + log b = log (ab)
now, log 3+ log 25 = log (3 times25)
= log 75

Answer 23

i understand now.thx

Answer 24

you are welcome.

Answer 25

solve log base x (5x+24)=2

Answer 26

x = 8 or -3

Answer 27

since logs are not defined for negative numbers, x = 8

Answer 28

do you know how I arrived at the answer, leona?

Answer 29

?how did u work it out

Answer 30

do you know how logarithms work?

Answer 31

i know some of the rules

Answer 32

tell me what you know about logs? what do you understand by logs?

Answer 33

i know that the logarithm of 1 regardless of the base is one

Answer 34

if i told you log 32 to the base 4 is 2.5, what do I mean by that?

Answer 35

that 4 ^2.5 is 32

Answer 36

exactly! good!
have you tried that in your calculator?

Answer 37

yes

Answer 38

so you understand that any number can be represented as a power of another number?

Answer 39

yes

Answer 40

okay good. so what do i mean when i say log(5x+24) to the base x is 2?

Answer 41

it means that x raise to the power 2 equal (5x+24)

Answer 42

I should have said any POSITIVE number can be represented as apower of any other number (the base)

Answer 43

right,
so x^2 = 5x+24

Answer 44

this is a simple quadratic equation

Answer 45

should i square the x^2?

Answer 46

why would you want to do that?

Answer 47

i dont know how to remove the x

Answer 48

okay have you solved quadratic equations before?

Answer 49

yes

Answer 50

can you see that x^2 = 5x+24 can be rearranged so that it is in the form
ax^2+bx+c = 0?

Answer 51

ohh yea

Answer 52

after that it is straightforward factoring. Remember that you will get a negative root. You cannot use the negative root, because as I explained before, logarithms for negative bases are generally discarded.

Answer 53

what r the two factors? cant find them

Answer 54

post your equation.

Answer 55

x^2-5x-24=0

Answer 56

i got 8

Answer 57

yeah!!!!!!

Answer 58

did you use the quadratic formula or the factoring method?

Answer 59

quadratic

Answer 60

okay. anything that works, although in this case factoring is more elegant and efficient.
remember, you have to discard the x= -3 root

Answer 61

i did

Answer 62

okay, do you know the reason why you discarded -3?

Answer 63

because log not defined for negative numbers

Answer 64

no, its because logs with negative bases only work for even powers.
anyway, good job! have a medal.

Answer 65

ok thank you

Answer 66

do a little homework assignment for me. Google "why logarithms are not defined for negative bases"
and "why logarithms are not defined for negative numbers".
it will help you understand logs much better.
all the best!

Answer 67

you are welcome.

Answer 68

ill do that

Answer 69

:)

Answer 70

are u going to be online in the night?

Answer 71

i dont know. I generally come here in my free time to help out.

Answer 72

ohh cause i ave exam 2marow and i need more help with other topics

Answer 73

oh.. you can post your questions here so that I get notifications and I'll try to answer them before tomorrow.

Answer 74

ok am going to try this question log base x (5x+14)=2

Answer 75

okay, lemme know how it works out. you should get 7

Answer 76

logarithm are not defined for negative values because the log and In graphs have a vertical asymptotic line at x=0 which is the lower boundary of the graph ..in fact the limit as x approaches zero from the right hand side ,the function approaches infinity and that makes the zero point the maximum tolerable value for the x values less than zero

Answer 77

i got 7....using the factoring method

Answer 78

okay good.

Answer 79

thank you

Answer 80

your latest logarithm question will go like : \[5x +14=x^{2}\]

Answer 81

so \[x ^{2}-5x-14=0 and then you solve with the quadratic formula \]

Answer 82

need help with this 1....log base 4 (1) +log (25)

Answer 83

so x= 7 or x=-2 but when you substitute the x=-2 the equation doesnt make sence so x=7 is the answer
hope that was helpful

Answer 84

okay, what does log base 4 (1) mean?

Answer 85

log to base 4 to a number = 1

Answer 86

log base 4 of 1 means what power will you raise the number 4 to have a value of 1 so its like : 1=4\[^{x}\]

Answer 87

it means that 4 raised to a number should be equal to 1.
what is that number? we know that any number raised to the power 0 is 1. so log base 4 (1) is 0.
so your equation simplifies to just log 25

Answer 88

like 4\[4^{x}=1 \]

Answer 89

that means x=0

Answer 90

because

Answer 91

\[4^{0}\]

Answer 92

ohh yeah thats a rule of logs

Answer 93

yes. you should remember the basic rules of logs. Also, understand what logarithms mean. That way, even if you get stuck in your test, you can work it out.

Answer 94

so 5^2=25

Answer 95

right, log 25 = log 5^2 = ?

Answer 96

yeah so the final answer is log 5^2=25

Answer 97

log 25 without a base specified means the base is a standard base of ten (10)

Answer 98

so are you saying that 10^25 = 5^2, leona?