Question

if log 2=m log 5=n and log 1400= p find log 7=?

Answer 1

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Answer 2

㏒ 7 = p-2n-3m

Step-by-step explanation:

Given

$\log 2=m$

$\log 5=n$

$\log 1400 = p$

or, $\log 1400 =\log(7\times 2\times 100)$

or, $\log 1400 =\log(7\times 2\times 5^2\times 2^2)$

or, $\log 1400 =\log(7\times 5^2\times 2^3)$

or, $\log 1400 =\log 7+\log 5^2+\log 2^3$     ( ∵ ㏒ (m×n) = ㏒m+㏒n)

or, $p=\log 7+2\log 5+3\log 2$       (∵ ㏒mⁿ = n㏒m)

or, $p=\log 7+2n+3m$

or, $\log 7=p-2n-3m$

Hope this answer is helpful.

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