How to find antilog with simple calculator?

Question

I know how to find log to base $10$ using simple calculator:

say if you want to find log of $12$ you can do as blow:

Step 1: $13$ times $\sqrt{\star} \implies 1.00030338$;
Step 2: subtract 1: $1.00030338 - 1 = 0.00030338$;
Step 3: Multiply by $3558 = 1.07942$.

Can I find $\operatorname{antilog}$ too?

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By simple calculator i mean this:

Answer 1

Using your calculator's square root key, you can approximate any antilog as closely as you like. Say you want $10^{1.234}$. You start by writing $$1.234 \approx 1 + \frac18 + \frac1{16} + \frac1{32} + \frac1{128}$$ which you can find by any of several straightforward methods. (If this isn't clear, leave a comment and I will explain it further.)

Then you can calculate $$\begin{align}10^{1/8} &= \sqrt{\sqrt{\sqrt{10}}}\\ 10^{1/16} &= \sqrt{10^{1/8}}\\ 10^{1/32} &= \sqrt{10^{1/16}}\\ 10^{1/128} &= \sqrt{\sqrt{10^{1/32}}} \\ \end{align}$$

and so on. Then $$10^{1.234} \approx 10\cdot 10^{1/8}\cdot 10^{1/16}\cdot 10^{1/32} \cdot 10^{1/128}.$$

You can be a little more clever than this. $1.234$ is almost, but not quite, $1 + \frac18 + \frac1{16} + \frac1{32} + \frac1{64}$, so you can get a much better approximationby writing $$1.234\approx 1 + \frac18 + \frac1{16} + \frac1{32} + \frac1{64} \color{red}{- \frac1{512}}$$

and then $$10^{1.234}\approx 10\cdot 10^{1/8}\cdot 10^{1/16}\cdot 10^{1/32}\cdot 10^{1/64}\color{red}{\div 10^{1/512}}.$$

Answer 2

Just do the reverse of what u did. Like if u want to find antilog of 2.345 Step-1 Take numbers after decimal : 0.345 Step-2 Divide it by 3558: 0.00009696459 Step-3 Add 1: 1.00009696459 Step-4 Square it 13 times: Press * and = 13 times: 2.218 (approx) Step 5- Now the number before decimal is used as power of 10 and multiplied to the answer: 2.218 *10^2 Final answer= 221.8 (You may also take the whole number -2.345 and use it in the method. But answer may vary!)