Question

How to expand log 385 to the base 10

Answer 1

We first get the prime factors of 385.

385 = 5 × 7 × 11

Using the logarithmic formula to represent this in logarithm form.

Formula :

㏒ₐᵇ = n

aⁿ= b

a = the base, b=number, n = power

In this case the powers are 5, 7 and 11

㏒₁₀x = 5

x = 10⁵

㏒₁₀y = 7

y = 10⁷

㏒₁₀z= 11

z = 10¹¹

Writing this in logarithm.

㏒₁₀10⁵+ ㏒₁₀10⁷+ ㏒₁₀10¹¹

This is the expansion of ㏒ 10 to the power of 385.



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Answer 2

Hi Friend !!!


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385 = 5×7×11

$log_{10}(385) \\ \\ = log_{10}(7 \times 5 \times 11) \\ \\ = log_{10}(5) + log_{10}(7) + log_{10}(11) \\ \\ hope \: it \: helps \: u$
:-)