Question

How do you solve \[{8^{2x}} = {8^{x + 7}}\] ?

Answer 1

Hint: This problem is related to the rules of powers and indices. The base is the same for both sides. So we can directly compare the powers or can equate them. After equating we will perform the necessary calculations to get the value of x. that will be the final answer.

Complete step-by-step answer:
Given that,
\[{8^{2x}} = {8^{x + 7}}\]
Now since the base is same we will equate the powers,
\[2x = x + 7\]
Taking the unknowns on one side,
\[2x - x = 7\]
On subtracting we get,
\[x = 7\]
This is the simple solution.
So, the correct answer is “\[x = 7\]”.

Note: Remember we cannot directly start solving the problem if both sides are not in the same form that is in indices form or are not having the same base to equate. Indices and powers are having different laws. We can see addition, subtraction, multiplication and division also in powers. Index or power also means how many times that particular base number is to be multiplied. But if the power is zero then the answer is not zero it is always 1. And for the power 1 it is the same number once.
Also note that in the case above if we express 8 as power of 2 will not change the answer because both sides have 8.