Find the value of $\log_{10} 3^{\frac{1}{18}}$ , where $\log 3 = 0.4771$ is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

295.055

275.055

285.055

265.055

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

To solve log₁₀3^1/18, we use the logarithmic property:

Property: log_b(x^a) = a × log_b(x).

Here, the given expression is log₁₀3^1/18. Using the property, we rewrite it as:

log₁₀3^1/18 = (1/18) × log₁₀(3).

Now, the value of log₁₀(3) is provided as log 3 value = 0.4771. Substituting this value:

log₁₀3^1/18 = (1/18) × 0.4771

Next, divide 0.4771 by 18:

(1/18) × 0.4771 = 0.0265055.

Thus, the final value of log₁₀3^1/18 is approximately 0.0265055.

Conclusion

The calculated result is 0.0265055. This calculation heavily relies on the given log 3 value, which is 0.4771. Understanding the logarithmic properties and correctly substituting the log 3 value is essential for solving such problems accurately.

Watch 3-min video & get full concept clarity