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If 3^x + 3^x + 3^x = 1, what is x?

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If 3^x + 3^x + 3^x = 1, what is x? [#permalink] New post   28 Feb 2020, 08:58
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If \(3^x + 3^x + 3^x = 1\), what is \(x\)?

(A) \(–1\)
(B) –\(\frac{1}{3}\)
(C) \(0\)
(D) \(\frac{1}{3}\)
(E) \(1\)
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A
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Bunuel
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Re: If 3^x + 3^x + 3^x = 1, what is x? [#permalink] New post   28 Feb 2020, 10:07
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Asad wrote:
If \(3^x + 3^x + 3^x = 1\), what is \(x\)?

(A) \(–1\)
(B) –\(\frac{1}{3}\)
(C) \(0\)
(D) \(\frac{1}{3}\)
(E) \(1\)


\(3^x + 3^x + 3^x = 1\);

\(3*3^x = 1\);

\(3^{x + 1}= 1\);

\(x + 1 = 0\);

\(x = -1\).

Answer: A.
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vanam52923
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Re: If 3^x + 3^x + 3^x = 1, what is x? [#permalink] New post   28 Feb 2020, 10:12
Bunuel wrote:
Asad wrote:
If \(3^x + 3^x + 3^x = 1\), what is \(x\)?

(A) \(–1\)
(B) –\(\frac{1}{3}\)
(C) \(0\)
(D) \(\frac{1}{3}\)
(E) \(1\)


\(3^x + 3^x + 3^x = 1\);

\(3*3^x = 1\);

\(3^{x + 1}= 1\);

\(x + 1 = 0\);

\(x = -1\).

Answer: A.

why have u equated to 0\
1^100 is also 1 so why it cant be '
x+1=100
x=99.
yes though it ll make qsn statemnt false but whats the reasoning behind this
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Bunuel
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Re: If 3^x + 3^x + 3^x = 1, what is x? [#permalink] New post   28 Feb 2020, 10:18
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vanam52923 wrote:
Bunuel wrote:
Asad wrote:
If \(3^x + 3^x + 3^x = 1\), what is \(x\)?

(A) \(–1\)
(B) –\(\frac{1}{3}\)
(C) \(0\)
(D) \(\frac{1}{3}\)
(E) \(1\)


\(3^x + 3^x + 3^x = 1\);

\(3*3^x = 1\);

\(3^{x + 1}= 1\);

\(x + 1 = 0\);

\(x = -1\).

Answer: A.

why have u equated to 0\
1^100 is also 1 so why it cant be '
x+1=100
x=99.
yes though it ll make qsn statemnt false but whats the reasoning behind this


\(a^0=1\) Any nonzero number to the power of 0 is 1.
For example: \(5^0=1\) and \((-3)^0=1\)

8. Exponents and Roots of Numbers



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
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If 3^x + 3^x + 3^x = 1, what is x? [#permalink] New post   29 Feb 2020, 04:30
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Asad wrote:
If \(3^x + 3^x + 3^x = 1\), what is \(x\)?

(A) \(–1\)
(B) –\(\frac{1}{3}\)
(C) \(0\)
(D) \(\frac{1}{3}\)
(E) \(1\)


Another way of looking at it would be :
3* 3^x =1

3^x=1/3

3^x=3^-1

x=-1

Ans: (A)
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TheModo
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Re: If 3^x + 3^x + 3^x = 1, what is x? [#permalink] New post   20 May 2020, 14:29
3^x + 3^x + 3^x = 1

3^x(1+1+1) = 1

3^x(3) = 1

3^x = 1/3

1/(3^-x) = 1/3

-x = 1

x = -1
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Re: If 3^x + 3^x + 3^x = 1, what is x? [#permalink] New post   24 May 2020, 08:14
Expert Reply
Asad wrote:
If \(3^x + 3^x + 3^x = 1\), what is \(x\)?

(A) \(–1\)
(B) –\(\frac{1}{3}\)
(C) \(0\)
(D) \(\frac{1}{3}\)
(E) \(1\)



Solution:

Simplifying, we have:

3^x(1 + 1 + 1) = 1

3^x * 3 = 1

3^x = 1/3

3^x = 3^-1

x = -1

Alternate Solution:

3^x + 3^x + 3^x = 1

Note that we are adding 3^x three times, so we have 3 * 3^x on the left side:

3 * 3^x = 1

3^1 * 3^x = 1

Since 1 = 3^0, we have:

3^(1 + x) = 3^0

1 + x = 0

x = -1

Answer: A
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Re: If 3^x + 3^x + 3^x = 1, what is x? [#permalink]
24 May 2020, 08:14
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