2^x=1,find x

Question

2^x=1,find x

Answer 1

First of all, a⁰ = 1 where a is any real number.

 

If you want to work it out, you can take the natural log of both sides:

 

ln(2^x) = ln(1)

 

ln(1) = 0, so

 

ln(2^x) = 0

 

One of the properties of logarithms is that ln(a^b) = bln(a), so

 

xln(2) = 0

 

Divide both sides of this equation by ln(2). We then get

 

x = 0