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Finding unknown indices 
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#1
May103, 03:34 AM

P: 9

I would be grateful if someone could tell me how to find unknown indices.
e.g 3^x=9 (i know it is 2 but i would like to know the process for use with larger numbers). Thankyou in advance 


#3
May103, 05:37 AM

P: 333

No, you used the fact x=2.
9 = 3^x log 9 = log (3^x) log 9 = x log 3 x = log9/log3 = 2 log can be to any base as long as they are the same. you will usually find base 10, or base e on your calculator. log base e is usually ln. 


#4
May103, 05:48 AM

P: 321

Finding unknown indices
As long as we can think of the relationship between 3 and 9, we can solve this problem without using logarithm, like the one suggested by enslam. here are more examples (solve for x) 2) 5^{x} = 625 3) 4*5^{x} = 100 4) 2^{x} = 8 If you use Logarithm, in the step log9/log3, you need to know the fact that 9 = 3^2 too, unless you use a caculator. 


#5
May103, 06:50 AM

Math
Emeritus
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Thanks
PF Gold
P: 39,682

To solve, for example 3^{x}= 7, you will need to use logarithms. 


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