Log and Antilog Calculation | chemca

chemca.math

Part 1: Mult/Div Part 2: Roots Part 4: Log/Antilog

Advanced Skills

Log and Antilog Tricks

How to solve pH, Kinetics, and Electrochemistry problems without a calculator.

1. Values to Memorize (Base 10)

You only need to memorize Log 2, 3, 5, and 7. The rest can be derived.

x	log x (Approx)
2	0.30
3	0.48
4	0.60 ($2 \log 2$)
5	0.70

x	log x (Approx)
6	0.78 ($\log 2 + \log 3$)
7	0.85
8	0.90 ($3 \log 2$)
9	0.95 ($2 \log 3$)

$\ln x = 2.303 \log x$

2. Calculating Logarithms

Standard Format Method

Convert any number to scientific notation: $m \times 10^n$.

$$ \log(m \times 10^n) = n + \log m $$

Ex 1: Find $\log(400)$
$400 = 4 \times 10^2$
$\log(4 \times 10^2) = 2 + \log 4$
$= 2 + 0.60 = 2.60$

Ex 2: Find $\log(0.003)$
$0.003 = 3 \times 10^{-3}$
$\log(3 \times 10^{-3}) = -3 + \log 3$
$= -3 + 0.48 = -2.52$

Ex 3: Approximation (e.g., log 4.5)
4.5 is halfway between 4 and 5.
$\log 4 = 0.60$, $\log 5 = 0.70$.
$\log 4.5 \approx 0.65$

3. Calculating Antilog

Splitting Method

Antilog is simply $10^x$. Break the number into an Integer and a Decimal part.

Case A: Positive Numbers

Example: Antilog(3.6)

1. Split: $3 + 0.6$
2. Convert Integer to power: $10^3$
3. Convert Decimal to number: Which $\log x \approx 0.6$? $\rightarrow 4$.
4. Combine: $4 \times 10^3$

Case B: Negative Numbers (Common in pH)

Example: Antilog(-4.3)

Problem: Mantissa (decimal part) must be positive.

1. Add and subtract 1 to the integer part to make decimal positive.
2. $-4.3 = -4 - 0.3 = (-4 - 1) + (1 - 0.3)$
3. $= -5 + 0.7$
4. Convert Integer (-5) to power: $10^{-5}$
5. Convert Decimal (0.7) to number: Which $\log x \approx 0.7$? $\rightarrow 5$.
6. Combine: $5 \times 10^{-5}$

pH Calculation Tip: If $pH = 4.3$, then $[H^+] = \text{Antilog}(-4.3)$.
Shortcut: Next integer is 5. $10^{-5}$.
Difference is $5 - 4.3 = 0.7$. Antilog(0.7) is 5.
Result: $5 \times 10^{-5}$.

Speed Test

© 2026 chemca.in. Optimized for Science Students.

Quiz Revision Notes Downloads Class Notes Video Lectures