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Here's your answer...
Lets use some logic here.
Our main goal here is to eliminate the log, so that we get a rational number. If the log becomes log a base a, then it would be equal to 1. So, we need to convert those terms to a.
The base is simple. Its a^1/2. By logarithmic law, the power of the base can be taken out and its reciprocal will be multiplied to the log, so the number multiplied to this log will be 1/(1/2) = 2.
The other part requires a bit of thought. There are 5 roots. When powers there are taken out, they are directly multiplied. So the number coming out would be having a denominator of 2^5, or 32. Since the numerator is already multiplied by 2 (in the last paragraph), the denominator of the value comes as 16. This is enough to draw the conclusion that the second option is correct. However, I'm really bored right now, so I'll also tell you how that 31 came. Bonus for you!
When the outermost root will be removed, nothing will happen to the numbers. But when the next root is removed by squaring, there is already an a outside the root, so it will become a^2. When each successive root is removed, the a's outside will get squared. The value when all the roots are removed will come as a^16 * a^8 * a^4 * a^2 * a = a^31. This 31 is removed from a's power and multiplied with the fraction outside the log.
So, it would look like this...
(31*2/32) log a base a
Which will become 31/16.
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Here's your answer...
Lets use some logic here.
Our main goal here is to eliminate the log, so that we get a rational number. If the log becomes log a base a, then it would be equal to 1. So, we need to convert those terms to a.
The base is simple. Its a^1/2. By logarithmic law, the power of the base can be taken out and its reciprocal will be multiplied to the log, so the number multiplied to this log will be 1/(1/2) = 2.
The other part requires a bit of thought. There are 5 roots. When powers there are taken out, they are directly multiplied. So the number coming out would be having a denominator of 2^5, or 32. Since the numerator is already multiplied by 2 (in the last paragraph), the denominator of the value comes as 16. This is enough to draw the conclusion that the second option is correct. However, I'm really bored right now, so I'll also tell you how that 31 came. Bonus for you!
When the outermost root will be removed, nothing will happen to the numbers. But when the next root is removed by squaring, there is already an a outside the root, so it will become a^2. When each successive root is removed, the a's outside will get squared. The value when all the roots are removed will come as a^16 * a^8 * a^4 * a^2 * a = a^31. This 31 is removed from a's power and multiplied with the fraction outside the log.
So, it would look like this...
(31*2/32) log a base a
Which will become 31/16.
[0100100101]...More questions detected...[1001001001]
[01010101001]...Moving on to more queries...[0101010101011]
//Bot UnknownDude moving on to more questions
//This is your friendly neighbourhood UnknownDude
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