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Sub 505 (Easy)|   Exponents|      
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Bunuel
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If 5^x = 26, then 5^(2x) = 16 Nov 2020, 10:00
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C
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5% (low)

Question Stats:

88% (00:57) correct 12% (01:27) wrong based on 86 sessions

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If \(5^x=26\), then \(5^{2x}=\)


A. 5.2

B. 52

C. 676

D. 1881

E. 11,881,376
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C
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If 5^x = 26, then 5^(2x) = 16 Nov 2020, 10:56
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Bunuel
If \(5^x=26\), then \(5^{2x}=\)


A. 5.2

B. 52

C. 676

D. 1881

E. 11,881,376
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\(5^{2x}=5^x*5^x = 26*26 = 676\), Answer must be (C)
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If 5^x = 26, then 5^(2x) = 16 Nov 2020, 13:25
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5^x = 26
5^2x = (5^x)^2 = 26^2
= 26×26 = 676
Correct option is C.

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AliciaSierra
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If 5^x = 26, then 5^(2x) = 16 Nov 2020, 15:40
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Bunuel,

I agree with above posters that \(5^{2X}= 676\) I'm wondering what will be value of X if \(5^x=26\)
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Bunuel
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If 5^x = 26, then 5^(2x) = 17 Nov 2020, 00:07
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AliciaSierra
Bunuel,

I agree with above posters that \(5^{2X}= 676\) I'm wondering what will be value of X if \(5^x=26\)
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You don't need to find the value of x to answer the question. If still interesting x = log(26)/log(5) (x≈2.0244).
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kriswati
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If 5^x = 26, then 5^(2x) = 17 Nov 2020, 00:43
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While the above method i.e. \(26^2\) is easiest way to answer, logically we can also think of 26 as \((5^2+ 5^0)\).

while squaring i.e.\( (5^2+5^0)^2 \)we get \((a+b)^2=a^2+b^2+2ab\)

i.e. \((5^2)^2+(5^0)^2+2*5^2*5^0 =625+1+2*25=676\)
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If 5^x = 26, then 5^(2x) = 17 Nov 2020, 01:12
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5^x = 26
5^2x = (5^x)^2 = 26^2

26*26 =676
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If 5^x = 26, then 5^(2x) = 17 Nov 2020, 12:06
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1) If 5^x = 26, then x is pretty dang close to 2 since 5^2 = 25
2) Then 5^2x will be a bit greater than 5^4. 5^4 = 625
3) We know the answer is not exactly 4, rather it is slightly higher. 676 is the only answer choice that is even close to 625.
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