Using approximations & the laws of log to perform this calculation?

Question

I have to use the given approximation and the laws of logarithms to simplify this calculation:

$\sqrt{1.44}$ ; log $1.728 ≈ 0.23754$

I started off with using log on $\sqrt{1.44}$:

log($\sqrt{1.44}$)

log($1.44^{1 \over 2})$

$0.07918$

= log $1.2$

Now, I'm not sure what I can do with log $1.2$ and log $1.728$ so that I can get the textbook answer of $1.2$.

Answer 1

$\log 1.2 = \dfrac 13 \log(1.2^3) = \dfrac 13 \log 1.728 \approx 0.07918$

according to Wolfram|Alpha $10^{0.0798} = 1.199997\dots$

Answer 2

Hint:

$$1728=12^3\iff 1.728=\dfrac{1728}{1000}=\left(\dfrac{12}{10}\right)^3$$

The problem is reduced to putting in the numbers in $\log(\sqrt{1.44})=\log(1.2)=1/3\cdot\log(1.728)$. Can you proceed?