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If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?

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If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?  [#permalink]

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New post 12 Mar 2020, 06:23
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If \(\frac{1}{5^x}\) + \(\frac{20}{5^{x+1}}\) = \(25^x\), what is the value of x?

a) \(\frac{1}{2}\)

b)\(\frac{1}{3}\)

c)\(\frac{1}{4}\)

d)\(\frac{1}{5}\)

e)\(\frac{1}{6}\)
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Re: If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?  [#permalink]

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New post 12 Mar 2020, 06:36
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I got the correct answer but not sure if I did the appropriate steps

\(\frac{1}{5^x}\)+\(\frac{20}{5^{x+1}}\) = 25^x

\(\frac{1}{5^x}\)+\(\frac{5 * 2^2}{5^{x+1}}\) =\(5^{2x}\)

\(\frac{1}{5^x}\)+\(\frac{5^x}{2^{-2}}\) =\(5^{2x}\)

\(5^{-x}\)+\(\frac{5^x}{2^{-2}}\)=\(5^{2x}\)

pull out \(5^{-x}\)

\(5^{-x}\) \((1+\frac{-1}{2^{-2}})\)=\(5^{2x}\)

\(1+\frac{-1}{2^{-2}}\) = 5

\(5^{-x}\) * \(5^1\) = \(5^{2x}\)

\(-x+1 = 2x\)

\(1 = 3x\)

\(x = \frac{1}{3}\)

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Re: If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?  [#permalink]

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New post 12 Mar 2020, 06:48
whollymoses wrote:
If \(\frac{1}{5^x}\) + \(\frac{20}{5^{x+1}}\) = \(25^x\), what is the value of x?

a) \(\frac{1}{2}\)

b)\(\frac{1}{3}\)

c)\(\frac{1}{4}\)

d)\(\frac{1}{5}\)

e)\(\frac{1}{6}\)



A quick way would be
\(\frac{1}{5^x}\) + \(\frac{5*4}{5^{x+1}}\) = \(25^x\)..
\(\frac{1}{5^x}\) + \(\frac{4}{5^{x+1}*5^{-1}}\) = \(25^x\).....
\(\frac{1}{5^x}\) + \(\frac{4}{5^{x}}\) = \(25^x=5^{2x}\).....
\(\frac{5}{5^x}\) = \(5^{2x}\).....
\(5=5^{2x+x}=5^{3x}\)
Equating the powers
\(1=3x...x=\frac{1}{3}\)
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If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?  [#permalink]

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New post 12 Mar 2020, 06:51
whollymoses wrote:
If \(\frac{1}{5^x}\) + \(\frac{20}{5^{x+1}}\) = \(25^x\), what is the value of x?

a) \(\frac{1}{2}\)

b)\(\frac{1}{3}\)

c)\(\frac{1}{4}\)

d)\(\frac{1}{5}\)

e)\(\frac{1}{6}\)



\(\frac{1}{5^x}+\frac{20}{5^x*5}=5^{2x}\)

\(\frac{5}{5^x}=5^{2x}\)

\(5^{3x}=5\)

\(3x=1\)

\(x=\frac{1}{3}\)

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Re: If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?  [#permalink]

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New post 12 Mar 2020, 07:55
If \(\frac{1}{5^x}\) + \(\frac{20}{5^{x+1}}\) = \(25^x\), what is the value of x?

a) \(\frac{1}{2}\)

b)\(\frac{1}{3}\) --> correct: \(\frac{1}{5^x}\) + \(\frac{20}{5^{x+1}}\) = \(25^x\) => \(\frac{1}{5^x}\) + \(\frac{20}{(5^x*5^1)}\) = \(5^{2x}\) => \(\frac{5}{5^x}\) = \(5^{2x}\) => 1-x = 2x => x=\(\frac{1}{3}\)

c)\(\frac{1}{4}\)

d)\(\frac{1}{5}\)

e)\(\frac{1}{6}\)
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Re: If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?  [#permalink]

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New post 14 Mar 2020, 15:20
whollymoses wrote:
If \(\frac{1}{5^x}\) + \(\frac{20}{5^{x+1}}\) = \(25^x\), what is the value of x?

a) \(\frac{1}{2}\)

b)\(\frac{1}{3}\)

c)\(\frac{1}{4}\)

d)\(\frac{1}{5}\)

e)\(\frac{1}{6}\)


Getting common denominators, we have:

5/(5^x * 5) + 20/(5^x * 5) = 5^(2x)

25/(5^x * 5) = 5^2x

5/5^x = 5^(2x)

5^(1 - x) = 5^2x

1 - x = 2x

1 = 3x

1/3 = x

Answer: B
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Re: If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?   [#permalink] 14 Mar 2020, 15:20

If 1/5^x + 20/5^x+1 = 25^x, what is the value of x?

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