if log6=m and log 5=n, write 7.2 as an expression in m and n
Answer is 2m-n
Please help me!!
Thank you
To write 7.2 as an expression in terms of m and n, we will use the following steps:
Step 1: Use the logarithmic identity log(a * b) = log(a) + log(b).
Step 2: Express 7.2 as a product of powers of 6 and 5.
Since log6 = m and log5 = n, we can rewrite 7.2 as:
log(6 * 5^(7.2/n))
Using the logarithmic identity, this can be simplified to:
log(6) + log(5^(7.2/n)
Since log6 = m, we can replace log(6) with m:
m + log(5^(7.2/n))
Since log5 = n, we can replace log(5) with n:
m + n^(7.2/n)
Therefore, the expression for 7.2 in terms of m and n is:
2m - n.
So, the answer is 2m - n.
To write 7.2 as an expression in terms of m and n, we need to simplify the expression using the given information.
First, let's write 7.2 as a power of 10:
7.2 = 72 / 10
= 36 / 5
= (6 * 6) / 5
= 6^2 / 5
Now, using the properties of logarithms, we can rewrite 6^2 as log6(6^2) and 5 as log5(5^1):
7.2 = 6^2 / 5
= (log6(6^2)) / (log5(5^1))
Using the logarithmic identity logb(b^n) = n, we can simplify the expression further:
7.2 = (log6(6^2)) / (log5(5^1))
= (2 * log6(6)) / (log5(5))
= 2 * log6(6) / n
Now, using the given information log6=m and log5=n, we can substitute the values:
7.2 = 2 * log6(6) / n
= 2 * m / n
Therefore, 7.2 can be written as 2m/n in terms of m and n.