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| Math Central | Quandaries & Queries |
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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
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