SEARCH HOME
 Math Central Quandaries & 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,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.