Find the value of ${\log }_{10}{3}^{\frac{1}{18}}$, where $\log 3=0.4771$ is

To solve log1031/18, we use the logarithmic property:

Property: logb(xa) = a × logb(x).

Here, the given expression is log1031/18. Using the property, we rewrite it as:

log1031/18 = (1/18) × log10(3).

Now, the value of log10(3) is provided as log 3 value = 0.4771. Substituting this value:

log1031/18 = (1/18) × 0.4771

Next, divide 0.4771 by 18:

(1/18) × 0.4771 = 0.0265055.

Thus, the final value of log1031/18 is approximately 0.0265055.

Conclusion

The calculated result is 0.0265055. This calculation heavily relies on the given log 3 value, which is 0.4771. Understanding the logarithmic properties and correctly substituting the log 3 value is essential for solving such problems accurately.