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.

4=2^2

Then ln4=2ln2

3ln2=ln(2^3)=ln8

ln6=ln(2*3)=ln2+ln3.

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

Answer 6

Ln4-ln2

Answer 7

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