Question

Please help
Why there is no solution for log3(-4) ?

Answer 1

The domain of the log function is non-negative numbers.
The log of zero and the log of negative numbers are undefined.

Answer 2

Review the concept of domain. Mathstudent55 (above) has it right.

Answer 3

\(\large \color{black}{\begin{align}
& \log_{3}(-4)=x \hspace{.33em}\\~\\
& 3^{x}=-4 \hspace{.33em}\\~\\
& \text{which is not possible} \hspace{.33em}\\~\\
\end{align}}\)

Answer 4

Think of what log means.

\(\log_b x = y\) means \(b^y = x\)

The log of a number is the exponent you need to raise the base to, to get the number.
The \(\log_{10} 100 = 2\) since \(10^2 = 100\)

The log of a negative number could be written as this:

\(\log_{10} -100 = y\) means that \(10^y = -100\)

There is no exponent, y, that you can raise 10 to, to get -100.