logp 3 243 whats the value?

Question

i want the answer or method for solving this thing!

Answer 1

I'm guessing you mean that log₃(243) = p? If so, then we can solve it this way:

By saying that log₃(243) = p, what you are in effect saying is that 3^p = 243. Replace p with a succession of integers and you will find that p = 5.

But what if p isn't an integer? Say we have log₇(29) = p; then, the only way to exactly determine p is log(29)/log(7).

 

Answer 2

log(base 3) 243

= log(base 3) 3^5

= 5*log(base 3) 3

= 5

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The Four Basic Properties of Logs

logb (xy) = logb x + logb y.

logb (x/y) = logb x - logb y.

logb (xⁿ) = n logb x.

logb x = loga x / loga b.