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Write the powers to which the bases to be raised in the following. 

i) 64 = 2x

ii) 100 = 5ba

iii) \(\frac{1}{81}=3^c\)

iv) 100 = 102

v) \(\frac{1}{256}\) = 4a

1 Answer

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Best answer

i) 64 = 2x

We know that 

64 = 2 × 32 

= 2 × 2 × 16 

= 2 × 2 × 2 × 8 

= 2 × 2 × 2 × 2 × 4 

= 2 × 2 × 2 × 2 × 2 × 2 

64 = 26

⇒ x = 6

ii) 100 = 5b

Here also 100 cannot be written as any power of 5.

i.e., there exists no integer for b such that 5b = 100

iii) \(\frac{1}{81}=3^c\)

We know that 81 = 3 x 27 

= 3 × 3 × 9 

= 3 × 3 × 3 × 3 

= 34

∴ \(\frac{1}{81}=3^{-4}\) [∵a-3 = \(\frac{1}{a^m}\)]

∴ c = – 4

iv) 100 = 102

z = 2

v) \(\frac{1}{256}\)= 4a

We know that 256 = 4 × 64

= 4 × 4 × 16 

= 4 × 4 × 4 × 4 

∴ \(\frac{1}{256}\) = 4 

∴ a = – 4

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