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Solve using logarithm (root(4)(34.7))/(2.981)

Solve using logarithm 34.742.981 \frac{\sqrt[4]{34.7}}{2.981}

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Full solution

Q. Solve using logarithm 34.742.981 \frac{\sqrt[4]{34.7}}{2.981}
  1. Write Fourth Root: First, let's write the fourth root of 34.734.7 as 34.71/434.7^{1/4}.
  2. Logarithm Property: Now, we'll use the property of logarithms that log⁡(ab)=log⁡(a)−log⁡(b)\log(\frac{a}{b}) = \log(a) - \log(b). So, we'll take the logarithm of both the numerator and the denominator.
  3. Calculate Log of Numerator: Let's calculate the logarithm of the numerator: log⁡(34.71/4)\log(34.7^{1/4}). Using the power rule of logarithms, this is (1/4)⋅log⁡(34.7)(1/4)\cdot\log(34.7).
  4. Calculate Log of Denominator: Now, calculate the logarithm of the denominator: log⁡(2.981)\log(2.981).
  5. Subtract Logs: Subtract the log of the denominator from the log of the numerator to find the log of the entire expression.\newline(log⁡(34.71/4))−log⁡(2.981)=(14)log⁡(34.7)−log⁡(2.981)(\log(34.7^{1/4})) - \log(2.981) = (\frac{1}{4})\log(34.7) - \log(2.981).
  6. Calculate Values: Now, we'll use a calculator to find the values of log⁡(34.7)\log(34.7) and log⁡(2.981)\log(2.981). Let's say log⁡(34.7)≈1.540\log(34.7) \approx 1.540 and log⁡(2.981)≈0.474\log(2.981) \approx 0.474.
  7. Plug Values: Plug these values into our expression: (\frac{\(1\)}{\(4\)})\times \(1.540540 - 00.474474\.
  8. Divide by 44: First, divide 1.5401.540 by 44 to get 0.3850.385.
  9. Subtract Final Value: Now, subtract 0.4740.474 from 0.3850.385 to get the final value.\newline0.385−0.474=−0.0890.385 - 0.474 = -0.089.

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