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