What is the relationship between the number of significant figures in a number and the digits in the mantissa of its logarithmic form?

In a logarithmic calculation, why might a decimal point be crucial for determining the number of significant figures?

How many significant figures should the result of log(0.0123) have?

What is the anti-logarithm of 1.789, and how many significant figures should the result have?

Given log(x) = 0.345, calculate the value of x and ensure the result has the correct number of significant figures.