How to Find Antilog on a Calculator (Base 10 and Natural Log)

The short answer

The antilog (inverse logarithm) of a number x is 10 raised to the power x: antilog(x) = 10^x. So antilog(2.5) = 10^2.5 = 316.227766. On the Scientific Calculator, tap 1, 0, xʸ, 2, ., 5 and =. For a natural log (ln), the antilog is e^x instead, where e is about 2.718281828.

What antilog means

A logarithm answers "10 to what power gives this number?" The antilog goes the other way: "what number do I get if I raise 10 to this power?"

• log(1000) = 3, because 10^3 = 1000.
• antilog(3) = 10^3 = 1000.

They undo each other. That gives you a built-in check: take the log of your answer, and you should get back the number you started with.

There is no separate "antilog" button on most scientific calculators, including Lazyblink's. You use the power key, which is labelled xʸ.

How to find antilog step by step

Open the Scientific Calculator.

Tap 1 and 0 to enter the base 10.

Tap xʸ. The display shows 10^.

Enter the log value, for example 2.5.

Tap =.

The result is 316.227766. To check it, tap AC, then log, type 316.2, tap ) and =. You get 2.499961866, which is 2.5 allowing for the rounding in 316.2.

Remember to close the bracket after a function such as log(. If the expression is left open, the calculator shows Error.

Antilog of a negative number

Negative logs come up in chemistry (pH) and with numbers smaller than 1. Put the negative power in brackets so it is clear what is being raised:

Tap 1, 0, xʸ.

Tap (, then −, then 1, ., 3, then ).

Tap =.

antilog(−1.3) = 10^(−1.3) = 0.05011872336.

A negative log never gives a negative answer. It gives a number between 0 and 1. The antilog of any number is always positive.

Worked examples

Log value (x)	Antilog = 10^x
3	1000
2.5	316.227766
0.3010	1.99986187
3.7	5011.872336
−1.3	0.05011872336
−3.2	0.0006309573445

The 0.3010 row is a classic: log(2) is about 0.3010, so its antilog is almost exactly 2. The small difference comes from rounding log(2) to four decimal places.

Example: pH to hydrogen ion concentration

pH is defined as −log of the hydrogen ion concentration, so concentration = 10^(−pH). For a solution with pH 3.2:

10^(−3.2) = 0.0006309573445, or about 6.31 × 10⁻⁴ mol/L.

Example: decibels to a power ratio

A difference of D decibels corresponds to a power ratio of 10^(D ÷ 10). For 20 dB, type 10^(20÷10), which gives 100: the louder sound has 100 times the power.

Natural antilog: e^x

If your log was a natural log (ln, base e), the inverse is e^x, not 10^x.

• ln(4.481689) is about 1.5, so the natural antilog of 1.5 is e^1.5.
• On the calculator, type e's value: 2.718281828, then xʸ, 1, ., 5, =. The result is 4.481689069, which matches e^1.5 to nine significant figures.

Always check which log you started with. A value from log needs 10^x; a value from ln needs e^x. Using the wrong base is the most common antilog error.

Antilog in other bases

The same idea works for any base: the antilog of x in base b is b^x.

• Base 2 (common in computing): antilog₂(10) = 2^10 = 1024. Type 2, xʸ, 1, 0, =.
• Base e (natural log): e^x, as above. For example e^2 = 7.389056099.

If a question just says "antilog" with no base, it almost always means base 10.

Antilog in Excel or Google Sheets

Spreadsheets have no ANTILOG function either. Use one of these:

• =10^2.5 or =POWER(10, 2.5) for a base-10 antilog. Both return 316.227766.
• =EXP(1.5) for a natural antilog. It returns about 4.4817.
• =POWER(10, A2) to convert a whole column of log values, then fill down.

This is handy when you have many values to convert, such as a column of pH readings or log-transformed data that you want back in the original units.

The log table method (for exams without calculators)

Older textbooks and some exams use log tables, where a log is split into a characteristic (the whole number part) and a mantissa (the decimal part).

For antilog(2.5):

Characteristic = 2, mantissa = 0.5.

Look up 0.5 in the antilog table: about 3.162.

The characteristic tells you where the decimal point goes: multiply by 10^2. Answer: 316.2.

For negative logs, tables use "bar" notation. −1.3 is written as bar 2.7, because −1.3 = −2 + 0.7. Look up 0.7 (about 5.012) and multiply by 10^−2 to get 0.05012. The calculator answer above, 0.05011872336, agrees.

Troubleshooting

• Answer is far too big or too small. You probably typed 2.5 then xʸ then 10, which is 2.5^10 = 9536.74. The base 10 always comes first.
• "Error" on the display. Check that every ( has a matching ). If you get Error using the e key together with xʸ, type 2.718281828 instead.
• You need more decimal places. The calculator shows up to 10 significant figures, which is more than enough for school and most practical work.
• Mixed up with inverse trig. The sin⁻¹, cos⁻¹ and tan⁻¹ keys are inverse trigonometric functions, not antilogs.

Related reading

• How log, ln, powers and roots work on the same calculator: How to Use a Scientific Calculator.
• Getting wrong sine and cosine answers? Check the angle mode: Degrees vs Radians.