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5^-x+5^-x+5^-x
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30 Jan 2024, 02:26
30 Jan 2024, 02:26
Expert Reply
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Question Stats:
66% (00:53) correct
33% (00:26) wrong based on 6 sessions
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Joined: 11 Nov 2023
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Re: 5^-x+5^-x+5^-x
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30 Jan 2024, 10:29
30 Jan 2024, 10:29
1
Applying exponent identities, \(a^m*a^n = a^{m+n}\)
\(5^{-x}+5^{-x}+5^{-x}+5^{-x}+5^{-x} = 5 * (5^{-x}) = 5^1 * (5^{-x}) = 5^{1-x} = 1\)
Any nonzero number to the power of 0 is 1, so we can also say \(1 = 5^0\).
\(5^{1-x} = 5^{0}\)
When an exponential equation has the same base on each side (in this case, 5), the exponents (1-x and 0) must be equal.
\(1-x = 0\)
\(x = 1\)
\(5^{-x}+5^{-x}+5^{-x}+5^{-x}+5^{-x} = 5 * (5^{-x}) = 5^1 * (5^{-x}) = 5^{1-x} = 1\)
Any nonzero number to the power of 0 is 1, so we can also say \(1 = 5^0\).
\(5^{1-x} = 5^{0}\)
When an exponential equation has the same base on each side (in this case, 5), the exponents (1-x and 0) must be equal.
\(1-x = 0\)
\(x = 1\)
gmatclubot
Re: 5^-x+5^-x+5^-x [#permalink]
30 Jan 2024, 10:29
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