Suppose that ln7 = a and ln8 = b. Use properties of logarithms to write this logarithm in terms of a and b.
ln root5(56)
To write ln √(5) 56 in terms of a and b, we can use the properties of logarithms.
First, let's simplify the expression by using the properties of logarithms:
ln √(5) 56 = ln(56^(1/2) * 5^(1/2))
Next, we can use the property of logarithms that states ln(ab) = ln(a) + ln(b):
ln √(5) 56 = ln(56^(1/2)) + ln(5^(1/2))
Now, we can use the property of logarithms that states ln(a^b) = b * ln(a):
ln √(5) 56 = (1/2) * ln(56) + (1/2) * ln(5)
Since we are given ln(7) = a and ln(8) = b, we can substitute these values into the expression:
ln √(5) 56 = (1/2) * ln(56) + (1/2) * ln(5)
= (1/2) * b + (1/2) * ln(5)
Therefore, ln √(5) 56 can be written in terms of a and b as (1/2) * b + (1/2) * ln(5).