Hard GCSE Questions

Ok... So I've got a couple of questions that I don't know how to do:

1) Find 2 solutions to

x^2=2^x

I know the answers are 2 and 4, but I got these from Trial and Error - I'm just wondering how to work it out algebraically/using indices rules.

2) Using a calculator, solve

x^x=100

Once again, I've reached an answer of 3.597 using trial and error.

(edited 13 years ago)

Reply 1

cj_134

You need logarithms which you can learn in a level maths around core 2

Reply 2

Benmaster

Original post by cj_134

You need logarithms which you can learn in a level maths around core 2

'twas in a GCSE Textbook :confused:

Maybe you're supposed to use trial and error?

Reply 3

dknt

Original post by Benmaster

'twas in a GCSE Textbook :confused:

Maybe you're supposed to use trial and error?

Considering it's GCSE, the only way I can think of is using a numerical method, so trial and error seems the most likely.

Reply 4

DonBorat

Original post by Benmaster

Ok... So I've got a couple of questions that I don't know how to do:

1) Find 2 solutions to

x^2=2^x

I know the answers are 2 and 4, but I got these from Trial and Error - I'm just wondering how to work it out algebraically/using indices rules.

2) Using a calculator, solve