Question

log 5x ^4 express in terms of logx

Answer 1

To express \( \log(5x^4) \) in terms of \( \log(x) \), we can use the properties of logarithms.

1. **Product Rule**: \( \log(a \cdot b) = \log(a) + \log(b) \)
2. **Power Rule**: \( \log(a^b) = b \cdot \log(a) \)

Now, applying these properties step-by-step:

\[
\log(5x^4) = \log(5) + \log(x^4)
\]

Next, we apply the power rule to \( \log(x^4) \):

\[
\log(x^4) = 4 \cdot \log(x)
\]

Putting it all together, we have:

\[
\log(5x^4) = \log(5) + 4 \cdot \log(x)
\]

Therefore, the expression of \( \log(5x^4) \) in terms of \( \log(x) \) is:

\[
\log(5x^4) = \log(5) + 4\log(x)
\]