Answered

IDNLearn.com provides a seamless experience for finding and sharing answers. Our platform offers reliable and detailed answers, ensuring you have the information you need.

Use the Product Rule of Logarithms to write the completely expanded expression equivalent to [tex]\ln (6a \cdot 9b)[/tex]. Make sure to use parentheses around your logarithm functions [tex]\ln (x + y)[/tex].

Note: When entering natural log in your answer, enter lowercase "ln" as "In". There is no "natural log" button on the Alta keyboard.

Provide your answer below:

Sagot :

GinnyAnsweridn
Sure! Let's solve the problem step-by-step using the Product Rule of Logarithms.

The Product Rule of Logarithms states that for any positive numbers [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:

[tex]\[ \ln(x \cdot y) = \ln(x) + \ln(y) \][/tex]

We need to apply this rule to the expression [tex]\( \ln(6a + 9b) \)[/tex].

First, let's factor the expression inside the logarithm:

[tex]\[ 6a + 9b \][/tex]

Notice that we can factor out a 3 from both terms:

[tex]\[ 6a + 9b = 3(2a + 3b) \][/tex]

Now, we have:

[tex]\[ \ln(6a + 9b) = \ln(3(2a + 3b)) \][/tex]

According to the Product Rule of Logarithms, we can separate the logarithm of the product into the sum of logarithms:

[tex]\[ \ln(3(2a + 3b)) = \ln(3) + \ln(2a + 3b) \][/tex]

So, the completely expanded expression equivalent to [tex]\( \ln(6a + 9b) \)[/tex] is:

[tex]\[ \boxed{\text{In}(6a + 9b) = \text{In}(3) + \text{In}(2a + 3b)} \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.