I need help for this question. I also need an explanation.The answer says log3(3x^2) but I need an explanation.

1 + log3(x^2)

I'm not Carnak the Magnificent. What was the question, and how did you arrive at your answer?

We're willing to provide help, and even answers, but don't make us come up with the questions, too!!

1 + log3(x^2) is the question. I posted it up there.

I didn't get the answer. I looked at the back of the textbook for the answer.The answer from the back of the textbook was log3(3x^2). I just need to know how to get the answer.

log3(3) = 1

so,
1+log3(x^2) = log3(3) + log3(x^2)
= log3(3 * x^2)

To simplify the expression 1 + log3(x^2), we can use the logarithmic identity:

log_b(xy) = log_b(x) + log_b(y)

In this case, we have 1 + log3(x^2). We can rewrite x^2 as (x * x), so applying the logarithmic identity, we get:

1 + log3(x * x)

Using the identity again, we can split this into two separate logarithms:

1 + (log3(x) + log3(x))

Now, combining the two logarithms, we have:

1 + 2 * log3(x)

Since log3(3) = 1, we can rewrite 1 as log3(3):

log3(3) + 2 * log3(x)

Using the property of logarithms, we can rewrite this as a single logarithm:

log3(3 * x^2)

Which simplifies to:

log3(3x^2)

Therefore, the simplified expression for 1 + log3(x^2) is log3(3x^2).