Question

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

Answer 1

Answer:

$3\ln2 +6y=\ln(8e^{6y})$

Step-by-step 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;

$\ln(8e^{6y})$