Write the expression as a single natural logarithm. 3 ln x - 2 ln c

Solution:

Given, 3 ln x - 2 ln c

We have to write the expression as a single natural logarithm.

By log property,

m log(a) = log (a)m

So, 3 ln x = ln (x)3

2 ln c = ln (c)2

3 ln x - 2 ln c = ln (x)3 - ln (c)2

By log property,

ln (a) - ln (b) = ln (a/b)

So,  ln (x)3 - ln (c)2 = ln (x3/c2)

Therefore, the expression is  ln (x3/c2).

Write the expression as a single natural logarithm. 3 ln x - 2 ln c

Summary:

The expression 3 ln x - 2 ln c as a single natural logarithm is ln (x3/c2).

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