Question

Slove for n:(3 over 5 to the power of 2 ×25=3 n ​

Answer 1

n = 2

Explanation:

Hello!

Step 1: Expand the fraction

We can use the exponent rule to square 3/5.

• (
  `\frac35`)² =
  `(3^2)/(5^2)`
• 
  `(9)/(25)`

Step 2: Simplify

Now, we can multiply

• 
  `(9)/(25) * 25 = 3^n`
• 
  `9 = 3^n`

Now, we need to find how many times 3 is multiplied to get 9 ,and that would be 2

Answer 2

n = 2

Explanation:

Given equation:

`\left(\frac35\right)^2 * 25=3^n`

`\textsf{Apply exponent rule }\left((a)/(b)\right)^c=(a^c)/(b^c) :`

`\implies \left((3^2)/(5^2)\right) * 25=3^n`

`\textsf{Apply}\: \left((a)/(b)\right) * c=(ac)/(b) :`

`\implies (3^2\cdot 25)/(5^2)=3^n`

`\textsf{Apply}\:5^2=5 * 5=25:`

`\implies (3^2\cdot 25)/(25)=3^n`

Cancel the common factor 25:

`\implies 3^2=3^n`

`\textsf{If}\:a^(f(x))=a^(g(x)),\:\textsf{then}\:f(x)=g(x) :`

`\implies 2=n`