If we are given the base and answer how can we find the exponent value?

is there a method or a formula for this??


example


3x= 81


x being the exponent


how do we find out what x is?|||you would have to use logarithms





which is basically





Log with a subscript 3 (which means in base 3) of 81 [written normally]





overall that means, what exponant do i have to put to 3 to get 81


on calculator, the log bottom is automatically on log in base 10





u must use simple logarithmic properties and do





log 81 divided by log 3





answer is 4 btw|||3x3x3x3 = 81 so the answer is 4|||3^x= 81





Express 81 also as follows


81 = 3^4 using the same base 3





3^x=3^4





now on both sides bases are same





so the exponents are same too





This implies x = 4|||logarithms!





log(81)/log(3) means:


3 to which power is equal to 81|||Take the log of both sides.





log(3^x) = log(81)


x log(3) = log(81)


x = log(81)/log(3)


x = 4.394 / 1.099 = 4