Question

Solve the equation
log(x^4) = (log x)^2

Answer 1

\[\log(x^4) = (\log(x))^2\]

Answer 2

Power rule: \(\log(x^a) = a \cdot \log(x)\)

Answer 3

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

Answer 4

\(\large\tt \begin{align} \color{black}{log(x^4) = \left( log (x)\right )^2\\~\\
4logx = log( x)\times log (x)\\~\\
4 = log (x)\\~\\
log (x)=4 \\~\\
x=10^4 \\~\\
x=10000 \\~\\

}\end{align}\)

Answer 5

It still says it is wrong

Answer 6

really?

Answer 7

What is the base??

Answer 8

it might be natural; log
which is represented
as
\(\Large ln(x)\)

\(\large\tt \begin{align} \color{black}{ln(x^4) = (ln x)^2\\~\\
4lnx = ln x\times ln x\\~\\
4 = ln x\\~\\
ln x=4 \\~\\
x=e^4 --------(\rm e=2.718)\\~\\
x=54.59 \\~\\

}\end{align}\)