Question

How do you solve \[{{2}^{3x+5}}=128\] ?

Answer 1

Hint: As we can see that the above equation is an exponential equation. In order to solve it we have to get a basic definition of exponents. First, we will try to simplify the given exponential equation such that we get the same bases on both sides of the equation. After that we will compare the powers on both sides of the equation as bases are equal on both the sides therefore, powers can be equated. Simplify further to get the value of x.

Complete step by step answer:
The above question belongs to the concept of exponential equations. These are the equations in which the variable occurs in the exponent or the power of the equation. Logarithmic equations are just the opposite or inverse of exponentiation. Thus, we can conclude that the logarithm of a given function is the exponent to which another number must be raised in order to get the original number and in order to convert a logarithmic function into exponential form we have to take inverse.
Now, in the question we have \[{{2}^{3x+5}}=128\]
First we will use different exponential rules in order to make the bases same on both sides. After that we will equate the powers from both the sides.
Therefore,
\[\begin{align}
  & {{2}^{3x+5}}=128 \\
 & \Rightarrow {{2}^{3x+5}}={{2}^{5}} \\
\end{align}\]
Equating powers on both the sides, we get
\[\begin{align}
  & \Rightarrow {{2}^{3x+5}}={{2}^{5}} \\
 & \Rightarrow 3x+5=5 \\
 & \Rightarrow 3x=0 \\
 & \Rightarrow x=0 \\
\end{align}\]
Hence \[x=0\] is the required answer.

So, the correct answer is “Option C”.

Note: While solving the above question keep in mind the basic exponential rules. This question can be solved using logarithms, we can take log on both sides and then solve. Before equating the powers, check whether the bases are the same or not. Try to perform each and every step.