Question

Find the value of 1.01^ ¾

Please don't give wrong answer for points .

Hope you understand

Answer 1

Value - 910 . 8775566

Answer 2

Answer:

1.005988

Step-by-step explanation:

Method 1 → Using Bionomial expansion

(1.01) $\frac{3}{4}$

= (1 + 0.01) $\frac{3}{4}$

= 1 + $\frac{3}{4}$ (0.01) + $\frac{\frac{3}{4}(\frac{3}{4} - 1)}{2!}$ (0.01)² + ....

= 1 + 0.0075 + $\frac{\frac{3}{4}(\frac{3 - 4}{4})}{2!}(0.0001)$

= 1 + 0.0075 + $\frac{1}{4} (0.0001)$

= 1 + 0.0075 + 0.000025

≈ 1.007525 (Approx)

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Method 2 → Using Logarithm

Let x  = $(1.01)^{\frac{3}{4} }$

Taking Log both side

=> log x = $\frac{3}{4}$ log (1.01)

=> log x = $\frac{3}{4}$ 0.004321 [log 1.01 = 0.004321 (using logarith table)

=> log x = 0.0025926

Taking Antilog both side

=> x = 1.005988

Hence, $(1.01)^{\frac{3}{4} }$ = 1.005988

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Amrit______