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

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

the middle term is log(25/4) not log(25/24)

the middle term is log(25/4) not log(25/24)

yeeeee....gotcha, the question i had was 25/24, rest all was same, and i couldn't solve it.....the question here is 25/4.....so for sure either this or the question in my today's exam was wrong. BTW i am sure the answer you got would be correct now as it aint 25/24 anymore, but my question paper still says that, HUH, wrong question, i should get full marks :D :D :D

i got the answer by taking the middle term as 5 log (25/24)

it is equal to log 2.. provided i am doing the calculations right. which i think i am..