Question

How do you evaluate ${\log _6}1$ ?

Answer 1

In questions like this, we can assume the value which needs to be calculated as x so that we can convert the equation from logarithmic form to exponential form and then we need to find a relation between left side of the equation and right side of the equation so that it makes a linear equation through which we can find the value of the variable x.

Complete step-by-step solution:
We are given to calculate the logarithmic expression ${\log _6}1$.
Let us assume ${\log _6}1$ as x.
So, $x = {\log _6}1$
Since we know that if a and b are positive real numbers and b is not equal to $1$, then ${\log _b}a = y$ is equivalent to ${b^y} = a$.
Using the above-mentioned property here, we will get:
$\Rightarrow {6^x} = 1$
Now, since we have to simplify the equation to solve it, we will try to make the base equal on both the sides. So, as we know that ${6^0} = 1$, we will substitute $1$ as ${6^0}$ so as to make the bases equal on both sides of the equation.
$\Rightarrow {6^x} = {6^0}$
Since the bases on both sides are the same, we can directly equate the exponential powers on them. So, now we can compare the powers of the variable on both sides of the equations.
We get, $x = 0$.
So, we get the value of x as $0$.

Hence the answer for he given question is ‘0’

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