Question

log 3x^5 express in terms of logx

Answer 1

To express \( \log(3x^5) \) in terms of \( \log(x) \), we can use the properties of logarithms:

1. The product property: \( \log(a \cdot b) = \log(a) + \log(b) \)
2. The power property: \( \log(a^b) = b \cdot \log(a) \)

Using these properties, we can break down \( \log(3x^5) \):

\[
\log(3x^5) = \log(3) + \log(x^5)
\]

Now, apply the power property to \( \log(x^5) \):

\[
\log(x^5) = 5 \cdot \log(x)
\]

Putting it all together:

\[
\log(3x^5) = \log(3) + 5 \cdot \log(x)
\]

So the expression for \( \log(3x^5) \) in terms of \( \log(x) \) is:

\[
\log(3x^5) = \log(3) + 5 \log(x)
\]