Question

Write the expression as a single natural logarithm 3 ln 2 + 6 y

Answer 1

`3\ln2 +6y=\ln(8e^(6y))`

Explanation:

The given logarithmic expression is

`3\ln2 +6y`

We can rewrite this as;

`3\ln(2) +6y\ln(e)`

Recall and use the power rule of logarithms.

`k\ln(a)=\ln(a^k)`

This gives us;

`\ln(2^3) +\ln(e^(6y))`

`\ln(8) +\ln(e^(6y))`

We now apply the product rule of logarithms;

`\ln(a)+\ln(b)=\ln(ab)`

We apply this rule to get;

`\ln(8e^(6y))`