Q.Using logarithms, evaluate $\dfrac{25.36 \times 18.5}{6.4}$. (Given $\log 25.36 = 1.4041$, $\log 18.5 = 1.2672$, $\log 6.4 = 0.8062$, and antilog $0.8651 = 7.331$.)

Taking the logarithm turns the product and quotient into additions and a subtraction, and a single antilog recovers the answer.

Let $x = \dfrac{25.36 \times 18.5}{6.4}$. Take logarithms (product and quotient laws):

Substitute the given table values:

Add the numerator logs: $1.4041 + 1.2672 = 2.6713$. Subtract the denominator log: $2.6713 - 0.8062 = 1.8651$. …

Cross-check by direct arithmetic. $25.36 \times 18.5 = 469.16$, and $469.16 \div 6.4 = 73.31$ (to 2 d.p.). The direct computation matches the logarithm re …

The commonest error is subtracting the denominator's logarithm from only one of the numerator terms, or adding it instead of subtracting — a division of numbers must become a subtraction of logarithms. Another is misplacing the decimal point a …