Question

Solve the given exponential equation.
5^(|x| − 1) = 125

Answer 1

so.... what's say.... \(\large 5^3 =?\)

Answer 2

125

Answer 3

so... ok... so we could say that \(\bf 5^{|x| - 1}=125\implies 5^{{\color{brown}{|x| - 1 }}}=5^{\color{brown}{ 3}}\qquad thus
\\ \quad \\
|x| - 1=3\)

so...is just a simple absolute value, solve for "x"

Answer 4

so |x|=4

Answer 5

hmm

Answer 6

\(\large {
|x|=a\to
\begin{cases}
+x=a\\
-x=a
\end{cases}\qquad thus\qquad
\\ \quad \\
|x|=4\to
\begin{cases}
+x=4\implies &x=4\\
-x=4\implies &x=-4
\end{cases}
}\)