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We don't need any special methods to see that

2x=4⇒x=22x=8⇒x=3

But what about the equation

2x=6

2^x with points

We can see from the graph that there should be an answer around x≈2.6 or so. So how do we find x?

What we need is an inverse function! If f is defined by

f(x)=2x,x∈R

then the solution to

f(x)=6

is

x=f−1(6)

This is where logarithms come in, as we will see in the next example.


Use logarithms to solve the following equations, giving your answers to 3 significant figures where necessary.

2x=8
2x=7
3x=127
52x+1=100