# Calculation method for the value of 13 to the 61th power and the number of digits [Easy]

Converting 13 to the 61th power to a value yields 89236903245680961916549731644772879118981920802965765857801986273213.

Below is the formula.

$13^{61}=$
89236903245680961916549731644772879118981920802965765857801986273213

Also, $13^{61}$ has 68 digits.

This page explains how to calculate $13^{61}$ and how to calculate the number of digits of $13^{61}$.

This site is created by Dr. Thomsontom labIt operates under the name

## Calculating 13 to the 61th Power

13 to the 61th power is simply 13 multiplied by 61 times.

Basically, the only way to find it is to repeat multiplication.

Then you can use google search.

For example, if you search for "14 to the 21st power" on google, a calculator will come up and tell you the answer.

Calculating the power in this way is difficult, so it is sometimes obtained as the first step.

Next, let's find the number of digits in $13^{61}$.

## Number of digits in 13 to the 61th power

Calculating $13^{61}$ gives us 68 digits.

### Find the number of digits in 13 to the 61th power

Let's calculate the common logarithm of 13 to the 61th power.

\begin{eqnarray}
\log_{10}13^{61}&=&61 \log_{10}13\\
&=&61\times 1.1139\cdots\\
&=&67.95
\end{eqnarray}

In other words,
We can say that $13^{61}=10^{67.95}$, so we know that $13^{61}$ has 68 digits.

### How to find the number of digits

To find the number of digits in $13^{61}$, use common logarithms.

By using the common logarithm, we can calculate the power of 10, so we know the number of digits.

For example, $10^1=10$ is 2 digits.
On the other hand, $10^2=100$, so 3 digits.

So $10^a$ has $10+1$ digits.
If $a$ is a decimal, the number of digits is the integer part plus 1.

$a=11.34$ will be 12 digits.

## power size quiz

Q1

Which one is bigger?

$12 ^ 5$

$5^{12}$

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