If log 6 = m and log 5 = n, write log 7.2 as an expression in m and n.

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justaguide eNotes educator | Certified Educator

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We can write 7.2 as 6*6/5

log 7.2 = log 6*6 / 5 = log 6^2 / 5

Now log (a^b) = b* log a and log (a/b) = log a - log b

log (6^2 / 5)

=> 2 log 6 - log 5

as log 6 = m and log 5 = n

=> 2m - n

Therefore log 7.2 = 2m - n

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giorgiana1976 | Student

We'll re-write the number 7.2 = 72/10

We'll simplify and we'll get:

72/10 = 36/5

We''ll take logarithms both sides:

lg 7.2 = lg (36/5)

We'll apply the quotient rule of logarithms:

lg(x/y) = lgx - lgy

lg (36/5) = lg 36 - lg 5

Lg 36 = lg 6^2 = 2lg 6 (power rule of logarithms)

lg 7.2 = 2lg 6 - lg 5

But lg 6 = m and lg 5 = n. We'll substitute and we'll get:

lg 7.2 = 2m - n

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