if log6=m and log 5=n, write 7.2 as an expression in m and n
Answer is 2m-n
Please help me!!
7.2=36/5
36=6*6
log(a+b=log(a)+log(b)
log(36)=log(6)+log(6)=2*log(6)
log(a/b)=log(a)-log(b)
log(36/5)=2*log(6)-log(5)
log(6)=m log(5)=n
log(36/5)=log(7.2)=2m-n
Third row have typefeler
Correct formula is:
log(a+b)=log(a)+log(b)
To write 7.2 as an expression in terms of m and n, we can use the logarithmic properties. First, let's express 7.2 as a logarithm using either base 6 or base 5:
Using base 6:
7.2 = 6^x
Using base 5:
7.2 = 5^y
To find the values of x and y in terms of m and n, we need to relate the given logarithmic expressions to the base of 7.2. Since 7.2 is not an exact power of 6 or 5, we need to use approximation.
Let's start with the expression log6 = m:
Take both sides to the power of 7.2:
6^(log6) = 6^m
Since any base raised to the power of its own logarithm is equal to the argument of the logarithm, we have:
6^m = 7.2
Now let's solve for m:
m = log6(7.2)
Similarly, using the expression log5 = n, we have:
n = log5(7.2)
Now, to express 7.2 in terms of m and n, we substitute these values back into the logarithmic expressions:
7.2 = 6^m = 6^(log6) = 6^(log6(7.2))
Using the logarithmic identity logb(b^x) = x, we can simplify:
7.2 = 7.2^(log6(7.2))
Similarly:
7.2 = 5^(log5(7.2))
Thus, we can write 7.2 as an expression in m and n:
7.2 = 6^(log6(7.2)) = 5^(log5(7.2))
Since log6(7.2) equals m and log5(7.2) equals n, we can simplify this expression further:
7.2 = 6^m = 5^n
Now, to express 7.2 in terms of m and n, we can use logarithmic properties once again. Taking the logarithm of both sides with base 6 gives us:
log6(7.2) = log6(6^m) = m
Similarly, taking the logarithm of both sides with base 5 gives us:
log5(7.2) = log5(5^n) = n
We can rearrange the equation log6(7.2) = m to solve for 7.2:
7.2 = 6^m
Substituting m = log6(7.2) into the expression, we get:
7.2 = 6^(log6(7.2))
Now, substituting n = log5(7.2) into the expression, we get:
7.2 = 5^(log5(7.2))
Therefore, we can simplify 7.2 as an expression in terms of m and n to:
7.2 = 6^(log6(7.2)) = 5^(log5(7.2)) = 6^m = 5^n
Further simplifying, we can write:
7.2 = 6^m = 5^n
Finally, combining the variables, we can express 7.2 as an expression in m and n as:
7.2 = 2m - n