Question
log 7x^3 express in terms of logx
Answers
GPT-4o mini
To express \(\log(7x^3)\) in terms of \(\log(x)\), we can use the properties of logarithms.
Using the logarithmic identity that states \(\log(ab) = \log(a) + \log(b)\) and \(\log(a^b) = b \log(a)\), we can decompose \(\log(7x^3)\) as follows:
\[
\log(7x^3) = \log(7) + \log(x^3)
\]
Now applying the power rule:
\[
\log(x^3) = 3\log(x)
\]
Putting it all together, we have:
\[
\log(7x^3) = \log(7) + 3\log(x)
\]
Thus, the expression for \(\log(7x^3)\) in terms of \(\log(x)\) is:
\[
\log(7x^3) = \log(7) + 3\log(x)
\]
Using the logarithmic identity that states \(\log(ab) = \log(a) + \log(b)\) and \(\log(a^b) = b \log(a)\), we can decompose \(\log(7x^3)\) as follows:
\[
\log(7x^3) = \log(7) + \log(x^3)
\]
Now applying the power rule:
\[
\log(x^3) = 3\log(x)
\]
Putting it all together, we have:
\[
\log(7x^3) = \log(7) + 3\log(x)
\]
Thus, the expression for \(\log(7x^3)\) in terms of \(\log(x)\) is:
\[
\log(7x^3) = \log(7) + 3\log(x)
\]