Qt - logarithms

 

 

using the property a*log b = log b^a we can write the above as log(16/15)⁷ + log (25/4)⁵ + log(81/80)³  and then using the property log a + log b + log c = log a*b*c.... 

we can write it as log (16/15)⁷* (25/4)^{5* (}81/80)³ and then solve..

it is equal to log2

since y² = xz, we can write it as y/x = z/y.

we are given:

a^x = b^y = c^z

taking log on the whole equation...

log a^x = log b^y = log c^z

using the property log x^y = y log x , the above equation can be written as 

x log a = y log b = z log c

now we make two cases 

x log a = y log b     and        y log b = z log c

log a / log b = y/x     and       log b / log c = z/y

log_ba = y/x      and      log_cb = z/y    

in the first line we are given that y/x = z/y

thus we get log_ba = log_cb

WOW....where did you get this question, I gave my b.com exam today and got this same question in it.....BTW I tried solving it in the paper as Aksh*ta suggested

 

log a + log b + log c = log a*b*c.... 

we can write it as log (16/15)⁷* (25/4)^{5* (}81/80)³ and then solve..

 

But I did not get the answer this way, later on my friends from maths background told me that to solve this we need to apply another law as

log a/b = log a - log b

 

Did not tried solving but as they told me that using this we will get a big figure whicih will ultimately be reduced because of the substraction sign and ultimately log 2 will remain.

 

So trying that i guess i should approach like...

-> ( 7 log 16 - 7 log 15 ) + ( 5 log 25 - 5 log 24 ) + ( 3 log 81 - 3 log 80 )

-> ( 7 log 2⁴ - 7 log 3X5 ) + ( 5 log 5² - 5 log 2³X3 ) + ( 3 log 3⁴ - 3 log 2⁴X5 )

-> ( 7 log 2⁴ - ( 7 log 3 + 7 log 5 ) ) + ( 5 log 5² - ( 5 log 2³ + 5 log 3 ) ) + ( 3 log 3⁴ - ( 3 log 2⁴ + 3 log 5 ) )

-> ( 7 log 2⁴ - 5 log 2³ - 3 log 2⁴ ) + ( - 7 log 3 - 5 log 3 + 3 log 3⁴ ) + ( - 7 log 5 + 5 log 5² - 3 log 5 )

 

Well believe me from this approach too am getting the wrong answer, am doing something wrong or maybe am missing a point somewhere.....solving the above will take you to the same answer i got today 1 / 2⁴ X 5⁷ X 3⁸ ---- something like this, am just recalling, but the bases are there the powers maybe wrong as I am not solving this damn thing again. I finished my exam way before time but was stuck on this for 45 mins on so and finally gave up, Even i wanna know the answer to this !!!

first one the final answer comes to log(2^6 * 3^5)

@ Tejaswi - log 5 in the denomaintor still exists, how did you cut it......recheck the answer please....is it the same, I'll have to solve it again then :O

it doesn't 7(4log2 -log3-log5) + 10(log5 - log2) + (3*(4log3 - 4log2 - log5)) = 28log2 -7log3-7log5+10log5-10log2 +12log3 -12log2-3log5 = 6log2 + 5log3 = log(64*243) I verified it on calculator it is correct

hi friends all the 3 problems are from 9th standard text book published by govt. of Andhra Pradesh.

hadd....i solved it again.....and got the answer as 1 / 2⁴ X 3⁷ X 5⁵ ........ i donno what to think......and seriously bcom mei itte lower level class 9th ke question aate hai and humse wo bhi ni bante....we planning for CA, hahaha

At Tejaswi.....how did you get this as the middle term 10(log5 - log2)..... it should be 5(2log 5 - 3log 2 - log 3) or (10log 5 - 15log 2 - 5log 3)

i just applied the properties.. and didnt solve it.. but now i did.. and i am getting the same answer as tejaswi....