Question

10x^2=2^x

Hi!

How do I go about solving an equation like this? It's meant to be a calculator solution but I'd love to know how it's done by hand. Logarithms maybe? .. Thank you in advance (:

Answer 1

10 x^2 = 2^x

ah
well, we will need the calculator or table to do the logs anyway but

log (10 x^2) = log 10 + 2 log x
if base ten logs
= 1 + 2 log x

log 2^x = x log 2
so

1 + 2 log x = x log 2

I need my slide rule or a calculator now :)

Answer 2

slide rule ?

Damon, you must be almost as old as I am.

Answer 3

Wolfram shows 3 real solutions

http://www.wolframalpha.com/input/?i=solve+10x%5E2%3D2%5Ex