Please explain why 2ln2=ln4 and why 3ln2 doesnt = ln6?
there’s a logarithm property that states:
n ln u= ln u^n
so 2 ln 2=ln 4 because 2^2=4, not because 2•2, equals 4.
3 ln 2= ln 2^3= ln 8
hope this makes sense.
For potended numbers of potence n log is the product of exponent and the logarithm for the number.
A number which is a product of two numbers has a logarithm like the sum of logarithm for the factors.
A ln B = ln (B^A)
That’s an identity that you should memorize.
Hence, 2ln2 = ln (2^2) = ln 4
3 ln 2 = ln (2^3) = 8
because a rule of logs is that loga^b = b*loga so therefore ln4 = ln2^2 so you can take the 2 to the front so 2ln2 = ln4 ln6 is NOT ln2^3 ln2^3 = ln8 3ln2 = ln8 hope this helps
Because the property is
aln(b) = ln(b^a)
2² = 4, 2³ = 8 ≠ 6
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