Question

PLEASE HELP WITH LOGs
IF loga5=2.32 and loga3=1.59, find loga45

Answer 1

so - note that 45 = 9*5

you have loga 5

and oyu have log a 3

what is the relationship betweem 3 and 9?

Answer 2

im not sure

Answer 3

2^2 = 4
3^2 = ?

Answer 4

9

Answer 5

SO 9 = 3^2

So if loga3 = 1.59
what is loga 3^2

Answer 6

would it be 3

Answer 7

no

this is the key point of th equestion

you must be studying logs and their properties so see if you can find a way of simplifying

\[\log _{a} x ^{n}\]

Answer 8

well that would be n times loga(x)

Answer 9

good - you have solved the question!

so what is

\[\log _{a }3^{^{2}}\]

Answer 10

2 times loga(3)

Answer 11

loga(5*3)

Answer 12

no - you want to find loga(5 * 3^2)

Answer 13

i mean 5*9

Answer 14

so loga(5)+loga(9)

Answer 15

you got it

and you have both those numbers.....

add em up!

Answer 16

but the answer key says 5.50 is that wrong?

Answer 17

no

you wrote just now what log 3^2 is (it is in YOUR post above...

what is log 9?
what is log 5

add tehm together

Answer 18

i got 2?

Answer 19

YOU wrote above

"well that would be n times loga(x)

so what is log 9 ( it is the same as log 3^2)

Answer 20

oh so 2 loga (3)

Answer 21

yes - you already wrote that

so now oyu can work out


loga(5)+loga(9)

Answer 22

but im typing that into my calculator and getting 2?

Answer 23

you don't need a calculator

you are given the numbers in the question

what is loga 3?
what is 2 loga 3?
what is loga 5?

soooo - what I slog a 45

you have DONE all the work - you just need to put the steps together

you are using the calculator wrong - but that doesn't matter now - you don't need the calculator

Answer 24

anyhow - you can't use calc because you don't know what a is

Answer 25

oh ok i forgot about the numbers so i got 5.5 with the number

Answer 26

thank you so much!

Answer 27

np

Answer 28

if it's not too much to ask, could you also help me with this last one? i have to condense \[\log_{4} 128-1\]

Answer 29

OK

it would be good if this was

log 4 x - log 4 y

Can you make it look like that?

Answer 30

i dont think we learned that

Answer 31

so if it was to look like I said tehn we can see that

log4 y = 1

what is y?
(think about the meaning of what loga really means) (I think you seem to have the skills to do this...)

Answer 32

do you mean y=128 or do you want it in exponential form?

Answer 33

no - it is not y=128

what is
\[\log_{10} 10\]
or
\[\log_{e} e\]

Answer 34

1?

Answer 35

yes

so logn n =1 for any n

so we can write your original equation as

log4 128 - log 4 4

can oyu simplify from there?

Answer 36

i got 32 but the answer is 5/2

Answer 37

because i did log4 128/4

Answer 38

ok - you have not quite done the simplification properly

what is log a - log b?

Answer 39

would you use the change of base property

Answer 40

no - sorry - I was being slack in notation - forget that

you are nearly there

go back to

log4 128 - log 4 4

can oyu simplify from there?
And try again - you made a small mistake....

Answer 41

log4 (128/4)?

Answer 42

yes

Answer 43

oh i got i! you convert it to exponential so you get 5/2

Answer 44

thanks so much!

Answer 45

not sure I follow that

Answer 46

log4 (128/4) = log4 (32) which IS 5/2

but I need to see how you got there....

Answer 47

i got 4^x =32 and then you do (2^2)^x=(2^5) and 2x=5 is 5/2

Answer 48

OK - I see


32 = 2^5

so 4^5 /4^2

Answer 49

yeah

Answer 50

well done

Answer 51

thanks so much!!