contestada

Use the Product Rule of Logarithms to write an expression equivalent to In(6a+ 9b). Make sure to use parenthesis around your logarithm functions In(x +y)

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xero099

Answer:

The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].

Step-by-step explanation:

Let be [tex]r = \ln (6\cdot a + 9\cdot b)[/tex], which is now solved as follows:

1) [tex]\ln(6\cdot a + 9\cdot b)[/tex] Given.

2) [tex]\ln [3\cdot (2\cdot a + 3\cdot b)][/tex] Distributive property.

3) [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex] ([tex]\ln (x\cdot y) = \ln x + \ln y[/tex]) Result.

The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].

facundo3141592

We want to find an equivalent expression to ln(6a + 9b). We will get:

ln(6a + 9b) = ln(3) + ln(2a + 3b)

Here we will be using the rule:

ln(x) + ln(y) = ln(x*y)

Now let's see our expression:

ln(6a + 9b) = ln(3*(2a + 9b))

Now we use the above rule to write:

ln(3*(2a + 3b)) = ln(3) + ln(2a + 3b)

Then the equivalent expression is:

ln(6a + 9b) = ln(3) + ln(2a + 3b)

If you want to learn more, you can read:

https://brainly.com/question/9280855

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