Question

convert from exponential to log form
t³ = m

Explanation:

Step1: Recall the exponential - logarithmic conversion formula

The general formula for converting an exponential equation \(a^{b}=c\) (where \(a>0,a
eq1\)) to logarithmic form is \(\log_{a}c = b\).

Step2: Identify \(a\), \(b\), and \(c\) in the given equation

In the given exponential equation \(T^{3}=m\), we can identify that \(a = T\) (the base of the exponential), \(b = 3\) (the exponent), and \(c=m\) (the result of the exponential operation).

Step3: Apply the conversion formula

Using the formula \(\log_{a}c = b\), substitute \(a = T\), \(b = 3\), and \(c = m\) into it. We get \(\log_{T}m=3\).

Answer:

\(\log_{T}m = 3\)