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# 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 (x^{3}/c^{2})

Therefore, the expression is ln (x^{3}/c^{2}).

## 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 (x^{3}/c^{2}).

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