Express as a single logarithm
ln(a)+1/2ln(b)
2ln4-ln2
ln a + (1/2) ln b
= lan a + ln )b^(1/2))
= ln (a√b)
you try the second, and let me know what you got
2ln4-ln2
=ln(16)-ln2
=ln(16/2)
=ln8?
correct
Thank you =)
We are asked to express 2+ln 2 as a single logarithm.Can somebody help me?
To express the given expressions as a single logarithm, we can use the properties of logarithms.
1) ln(a) + 1/2 ln(b):
We can use the property that states ln(a) + ln(b) = ln(ab).
Applying this property, we have:
ln(a) + 1/2 ln(b) = ln(a) + ln(b^(1/2)) = ln(a * b^(1/2))
2) 2ln(4) - ln(2):
We can use the property that states n ln(a) = ln(a^n).
Applying this property, we have:
2ln(4) - ln(2) = ln(4^2) - ln(2) = ln(16) - ln(2)
So, the expressions can be written as:
1) ln(a) + 1/2 ln(b) = ln(a * b^(1/2))
2) 2ln(4) - ln(2) = ln(16) - ln(2)
Note: It is important to simplify further if possible according to the given values of 'a' and 'b'.