Express as a simple logarithm 2ln6 – ln3

To simplify the expression \( 2\ln 6 – \ln 3 \) into a single logarithm, we can use the properties of logarithms.

First, we can use the power rule of logarithms, which states \( a \ln b = \ln(b^a) \):

2\ln 6 = \ln(6^2) = \ln(36)

Now, substitute this back into the expression:

2\ln 6 – \ln 3 = \ln(36) – \ln(3)

Next, we use the property of logarithms that states \( \ln a – \ln b = \ln\left(\frac{a}{b}\right) \):

\ln(36) – \ln(3) = \ln\left(\frac{36}{3}\right)

Simplifying \( \frac{36}{3} \):

\frac{36}{3} = 12

Therefore, we have:

2\ln 6 – \ln 3 = \ln(12)

So, the expression \( 2\ln 6 – \ln 3 \) can be expressed as:

ln(12)

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