Calculate the value of 32)/(185.4) using logarithms.

Rewrite the cube root as an exponent:

Apply the logarithm rule $\log(A^B) = B \log A$:

Apply the logarithm rules $\log\left(\frac{A}{B}\right) = \log A - \log B$ and $\log(AB) = \log A + \log B$:

Apply the logarithm rule $\log(A^B) = B \log A$ again:

• For $\log(36.72)$: Characteristic: 1 (since 36.72 has two digits before the decimal point, $2-1=1$). Mantissa: Look up 36 under 7 (which is 0.5647) and mean difference for 2 (which is 2). So, $\log(36.72) = 1.5647 + 0.0002 = 1.5649$.

• For $\log(0.46)$: Characteristic: $\bar{1}$ (since the first significant digit is in the first decimal place). Mantissa: Look up 46 under 0 (which is 0.6628). So, $\log(0.46) = \bar{1}.6628$.

• For $\log(185.4)$: Characteristic: 2 (since 185.4 has three digits before the decimal point, $3-1=2$). Mantissa: Look up $