Question

How do you solve $ {6^x} = 216 $

Answer 1

Hint: In this question, we are given a relation in which we have to find the value of $ x $ . For such questions, check that either if we can make the base of both the sides same. Then create the equivalent expressions and use the property that if bases are the same powers are also the same.

Complete step by step solution:
In the question, we are given an example of algebraic expression.
 $ {6^x} = 216 $ $ \left( 1 \right) $
Firstly, try to make the base of the two sides the same. Then we want to convert the $ 216 $ such that it would have base $ 6 $ . Then writing
  $ 216 = 6 \times 6 \times 6 $
We can also write it as
 $ 216 = {6^3} $ $ \ldots \left( 2 \right) $
Now, replacing the left-hand side of equation $ \left( 1 \right) $ with $ \left( 2 \right) $
 $ {6^x} = {6^3} $
Use the property of power, which states that if the bases are the same then powers are equal.
 $ \Rightarrow x = 3 $
So, the required answer is $ x = 3 $
So, the correct answer is “ $ x = 3 $ ”.

Note: For such questions, to make the base the same multiply the $ 6 $ with itself to make the base on the right-hand same. It contains such small steps to solve the question. For solving these questions, just remember the properties of power.