Question
Question: How do you solve \[{{25}^{2x+1}}=144\]?...
How do you solve 252x+1=144?
Solution
In the given equation 252x+1=144, the variable term is present as an exponent on the left hand side. So it cannot be solved by using the basic algebraic operations. For solving, we need to remove the variable from the exponent. For this we have to take the logarithm of both the sides of the equation. Then using the property logam=mloga, we will be able to remove the variable term from the exponent. Then we will obtain a linear equation in x which can be solved by using the basic algebraic operations.
Complete step by step solution:
The equation given in the above question is
⇒252x+1=144
Since the variable is present as an exponent, we cannot solve it directly. So in order to simplify the given equation, we take the logarithm on both the sides to get
⇒log(252x+1)=log144
Now, from the properties of the logarithm function we know that logam=mloga. Applying this property on the LHS of the above equation, we get
⇒(2x+1)log25=log144
Dividing both the sides by log25 we get
⇒2x+1=log25log144
Subtracting 1 from both the sides we get