Solve for the value of n: (2n)º = (3n-5)
The Correct answer and Explanation is:
To solve the equation (2n)∘=(3n−5)(2n)^\circ = (3n – 5)(2n)∘=(3n−5), we need to clarify what the symbol ººº signifies in this context. The most common interpretations could be degrees in terms of angle measures or the zero degree as a representation of the multiplicative identity in mathematical functions. However, since this appears to be an algebraic equation, we will interpret it as a standalone expression without specific implications of angle measures.
Starting from the equation:(2n)0=(3n−5)(2n)^0 = (3n – 5)(2n)0=(3n−5)
Since any non-zero number raised to the power of zero equals 1, we can simplify the left side:1=3n−51 = 3n – 51=3n−5
Next, we solve for nnn. We begin by isolating the term involving nnn:3n−5=13n – 5 = 13n−5=1
Now, add 5 to both sides to eliminate the constant term on the left:3n=1+53n = 1 + 53n=1+5
This simplifies to:3n=63n = 63n=6
To find nnn, divide both sides by 3:n=63=2n = \frac{6}{3} = 2n=36=2
Thus, the solution to the equation (2n)0=(3n−5)(2n)^0 = (3n – 5)(2n)0=(3n−5) is:2\boxed{2}2
Explanation
In this problem, we began with an equation involving an exponent. By recognizing that any number raised to the zero power is equal to 1, we simplified the equation significantly. After substituting this understanding into the equation, we were left with a linear expression in terms of nnn. Solving linear equations typically involves isolating the variable on one side by performing inverse operations (addition, subtraction, multiplication, division).
In this case, we performed a series of simple arithmetic steps: first adding 5 to both sides, resulting in a clearer linear equation. Then, dividing by 3 allowed us to isolate nnn. This process is fundamental in algebra and shows the importance of correctly interpreting exponents and isolating variables to find solutions efficiently.
The final result is that n=2n = 2n=2 satisfies the original equation, making it a valid solution.