Review question

# Can we find bounds for $\log_2 3$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9381

## Suggestion

Observe that $2^3 = 8$, $2^5 = 32$, $3^2 = 9$ and $3^3 = 27$. From these facts, we can deduce that $\log_{2}3$, the logarithm of $3$ to base $2$, is

1. between $1\frac{1}{3}$ and $1\frac{1}{2}$;

2. between $1\frac{1}{2}$ and $1\frac{2}{3}$;

3. between $1\frac{2}{3}$ and $2$;

4. between $2$ and $3$.

Can we create any inequalities from the information we’re given in the question?

Is it helpful to note that $\log_{2}x$ is an increasing function?