Answer :
Sure, let's solve the equation [tex]\(5^n \times 125 = 3125\)[/tex] step by step.
First, observe that [tex]\(125\)[/tex] can be written as a power of 5:
[tex]\[125 = 5^3\][/tex]
So, we can rewrite the equation as:
[tex]\[5^n \times 5^3 = 3125\][/tex]
Using the properties of exponents, we know that multiplying two numbers with the same base means we add their exponents:
[tex]\[5^{n+3} = 3125\][/tex]
Next, we need to express [tex]\(3125\)[/tex] as a power of 5:
[tex]\[3125 = 5^5\][/tex]
Now our equation is:
[tex]\[5^{n+3} = 5^5\][/tex]
Since the bases are the same, we can set the exponents equal to each other:
[tex]\[n+3 = 5\][/tex]
To solve for [tex]\(n\)[/tex], subtract 3 from both sides:
[tex]\[n = 5 - 3\][/tex]
[tex]\[n = 2\][/tex]
Therefore, the value of [tex]\(n\)[/tex] is:
[tex]\[n = 2\][/tex]
First, observe that [tex]\(125\)[/tex] can be written as a power of 5:
[tex]\[125 = 5^3\][/tex]
So, we can rewrite the equation as:
[tex]\[5^n \times 5^3 = 3125\][/tex]
Using the properties of exponents, we know that multiplying two numbers with the same base means we add their exponents:
[tex]\[5^{n+3} = 3125\][/tex]
Next, we need to express [tex]\(3125\)[/tex] as a power of 5:
[tex]\[3125 = 5^5\][/tex]
Now our equation is:
[tex]\[5^{n+3} = 5^5\][/tex]
Since the bases are the same, we can set the exponents equal to each other:
[tex]\[n+3 = 5\][/tex]
To solve for [tex]\(n\)[/tex], subtract 3 from both sides:
[tex]\[n = 5 - 3\][/tex]
[tex]\[n = 2\][/tex]
Therefore, the value of [tex]\(n\)[/tex] is:
[tex]\[n = 2\][/tex]
