Question

How do i distribute something to a natural log? for example, i have 6x(ln2+ln7) how do i distribute the 6x? does it get multiplied to the 2 and 7 or does it go in front of the log like 6xln2 + 6xln7. also how does 6ln2(x+3) distribute?

Answer 1

I hope it helps if you need a more detailed and simpler explanation let me know ;)

Explanation:

To distribute a coefficient to a natural logarithm expression, you can apply the distributive property. Let's break down the examples you provided:

Distributing 6x to ln(2) + ln(7): To distribute 6x to ln(2) + ln(7), you multiply 6x by each term inside the parentheses. The result will be 6x multiplied by ln(2) and 6x multiplied by ln(7). So, the distribution would be: 6x * ln(2) + 6x * ln(7). This can also be written as 6xln(2) + 6xln(7).

Distributing 6ln(2) to (x + 3): To distribute 6ln(2) to (x + 3), you multiply 6ln(2) by each term inside the parentheses. The result will be 6ln(2) multiplied by x and 6ln(2) multiplied by 3. So, the distribution would be: 6ln(2) * x + 6ln(2) * 3. This can also be simplified as 6ln(2)x + 18ln(2).

In both cases, the coefficient is distributed to each term inside the parentheses. Remember to apply the distributive property when distributing a coefficient to a natural logarithm expression.