Question

What is the value of n? if 3^10*27^2=9^2*3^n

Answer 1

just got an headache,a really bad one.

Answer 2

Where is n in the question?

Answer 3

^

Answer 4

its 3^n

Answer 5

Oh.

Answer 6

Sorry, right, here goes

Answer 7

3^7290 = 9^2*3^n
7290 log 3 = 2*3^n (log 9) (all base 10)
3645 log 3 = 3^n log 9
3^n = (3645 log 3/log 9)
n log 3 = log (3645 log 3/log 9)
n = (log (3645 log 3/log 9))/log 3

There we go, that should do it. Now we evaluate with a calculator. The principle I am using is that x^n = n log x.

Answer 8

Is that the correct method for solving these kinda questions?

Answer 9

its werid......Easy way is to make the powers on both side same and then equate powers

Answer 10

Can you solve? this question..Then I would understand how to solve these questions!!

Answer 11

\[ 3^(10)*27^2=9^2*3^n\]

3^10 * 3^6 = 3^4 * 3^n

16 =4+n

n=12

Answer 12

27 = 3^3

9 = 3^2

Answer 13

Got it!
Thanks..

Answer 14

Welcome..:)

Answer 15

Yeah, was just coming to post what @Yahoo! did. It's easier than you think, just convert all to base 3 and combine and you end up with something of the form\[\Large 3^a=3^b\]
Hence, a=b and it's an easy-peasy linear equation. :)