Question

You are given that 177147=3^11,
3^n=177147*9^5
Find the value of n

Answer 1

Answer: Rewrite the equation with the simplified form: 3^n = 177147 * 3^10.

Step-by-step explanation: To find the value of n in the equation 3^n = 177147 * 9^5, we can use the properties of exponents and simplify the equation step by step. 1. Simplify the right side of the equation: 177147 * 9^5 can be further simplified by recognizing that 9 = 3^2. So, 177147 * 9^5 = 177147 * (3^2)^5 = 177147 * 3^10. 2.

Answer 2

n = 5

Explanation:

To find the value of $$n$$ in the equation 3^n = 177147*9^5, we can start by simplifying the right side of the equation.

We know that 177147=3^11, so we can rewrite the equation as:

3^n = 3^11*9^5

Next, we can use the property of exponents that states a^m*b^n = (a*b)^(m+n) to simplify the right side of the equation:

3^n = (3^2*3^5)^5

3^n = (9*3^5)^5

3^n= (9*243)^5

3^n = 2187^5

Now, we can equate the exponents on both sides of the equation:

n = 5

Therefore, the value of n is 5.