Question

How would you write `\sqrt{36}=6` as a logarithmic equation?Important Note: to type a logarithm, start with the word log and to add the base use the underscore symbol _For example, to get `\log_{5}x=y` I typed this into an equation:"log_5 x=y"Underscore is SHIFT+MINUS on most keyboards.

Answer 1

EXPLANATION:

Given;

We are given the following equation;

$\sqrt{36}=6$

Required;

We are now required to write this as a Logarithmic equation.

Step-by-step solution;

To do this, we would first take the left side of the equation and simplify the radical;

$\sqrt{36}=36^{\frac{1}{2}}$

We now re-write the equation as shown below;

$36^{\frac{1}{2}}=6$

Now we can apply the log rule which is;

$\begin{gathered} If: \\ log_ba=c \\ Then: \\ b^c=a \end{gathered}$

For example;

$\begin{gathered} If: \\ log_{10}100=2 \\ Then: \\ 10^2=100 \end{gathered}$

Therefore we would now have;

$\begin{gathered} For\text{ }the\text{ }equation: \\ 36^{\frac{1}{2}}=6 \end{gathered}$

ANSWER:

$log_{36}6=\frac{1}{2}$