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Math  /  Algebra

QuestionGiven that log⁡(2)≈0.3010\log (2) \approx 0.3010, find the value of the logarithm. log⁡(2)\log (\sqrt{2}) □\square Need Help? Watch it

Studdy Solution

STEP 1

1. We are given that log⁡(2)≈0.3010\log(2) \approx 0.3010.
2. We need to find the value of log⁡(2)\log(\sqrt{2}).

STEP 2

1. Use the properties of logarithms to express log⁡(2)\log(\sqrt{2}) in terms of log⁡(2)\log(2).
2. Simplify the expression to find the value of log⁡(2)\log(\sqrt{2}).

STEP 3

Recall the logarithmic identity for roots:
log⁡(a)=log⁡(a1/2)=12log⁡(a)\log(\sqrt{a}) = \log(a^{1/2}) = \frac{1}{2} \log(a)
Apply this identity to log⁡(2)\log(\sqrt{2}):
log⁡(2)=12log⁡(2)\log(\sqrt{2}) = \frac{1}{2} \log(2)

STEP 4

Substitute the given value of log⁡(2)\log(2):
log⁡(2)=12×0.3010\log(\sqrt{2}) = \frac{1}{2} \times 0.3010

STEP 5

Calculate the expression:
log⁡(2)=0.1505\log(\sqrt{2}) = 0.1505
The value of log⁡(2)\log(\sqrt{2}) is:
0.1505\boxed{0.1505}

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