Suppose that ln2 = a and ln3 = b. Use properties of logarithms to write this logarithm in terms of a and b.
ln8
ln2 x ln2 x ln2
a + a + a (substitute)
3a
To write ln8 in terms of a and b, we can use the properties of logarithms.
First, let's express 8 as a power of 2:
8 = 2^3
Next, we can use the property that ln(ab) = ln(a) + ln(b):
ln8 = ln(2^3) = 3ln2
Since ln2 = a, we can substitute it into the equation:
ln8 = 3a
Therefore, ln8 can be written in terms of a as 3a.
To write ln8 in terms of a and b, we can use the properties of logarithms.
First, let's express 8 as a power of 2 since we know the value of ln2 (a).
8 = 2^3.
Now, using the property of logarithms that states ln(a^b) = b * ln(a), we can rewrite ln8 as:
ln8 = ln(2^3)
= 3 * ln2
= 3a
Therefore, ln8 can be written in terms of a as 3a.