Math CentralQuandaries & Queries


Question from Olivia:

How do you find the (b,n) if the solution of the equation 4^x=2^x+6 can be expressed at logb(n) where b and n are both prime numbers?

Hi Olivia,

Since $2^x$ and $4^x = (2^x)^2$ appear in the expression you have I think that log base 2 is what you need. Hence I would try $x = \log_2(n).$ Substitute this into the expression you have, simplify and solve for $n.$ Make sure you verify your answer.

Write back if you need more assistance,

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS