Question

If 5^2p+5^p+5^0=651, then p=​

Answer 1

Answer:

option a=2, b=3, c=4,d=5

Step-by-step explanation:

let start with option a

p=2 5^0=1

then, 5⁴+5²+1=651

625+25+1=651

Answer 2

Answer:  p is approximately 2.392.

Explanation:

We can start by simplifying the left side of the equation, 5(2p) + 5(p+1) = 651, in order to find p. We see that all of the terms have the same factor, 50, which is 1. Thus, the equation may be rewritten as follows:

5^(2p) + 5^p + 1 = 5^(0) * 651

When the right side of the equation is simplified, we obtain:

5^(2p) + 5^p + 1 = 651

We may now attempt to factor the equation's left side. We can factor out 5p because we see that it appears in just two of the terms:

5^p (5^p + 1) + 1 = 651

By taking away 1 from both sides, we obtain:

5^p (5^p + 1) = 650

We may now factor 650 into its prime components as follows:

650 = 2 * 5^2 * 13

5p must be a factor of 650 as it is found on the left side of the equation. The fact that 5p > 0 and that 2 * 52 * 13 must indicate that the factor must be bigger than 1. Hence, the only option is that 5p = 5p3, or 125. As a result, we have:

5^(2p) + 5^p + 1 = 651

5^(2p) + 125 + 1 = 651\s5^(2p) = 525

By multiplying both sides of the equation by their logarithms, we obtain:

Log(5(2p)) equals log (525)

Log(5) = 2p log (525)

P equals log(525/(2 log(5))

We determine using a calculator that:

p ≈ 2.392.

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