Use the One-to-One Property of Logarithms to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$2 \log x = \log 100$
A) $\{ 10 \}$
B) $\{ - 10 \}$
C) $\{ \pm 10 \}$
D) $\{ 5 \}$

Question

Quizplus · Accepted Answer

Using the One-to-One Property of Logarithms, we can simplify the equation to: 
\begin{align*}
2 \log x &= \log 100 \
\log x^2 &= \log 100 \
x^2 &= 100 \
x &= \pm 10 \
\end{align*}
However, since the original logarithmic expression has a domain of $x>0$, we must reject the solution $x=-10$. Therefore, the only solution in the given domain is $x=10$, which is choice A.

Use the One-To-One Property of Logarithms to Solve Logarithmic Equations 2log⁡x=log⁡1002 \log x = \log 1002logx=log100

Use the One-To-One Property of Logarithms to Solve Logarithmic Equations $2 \log x = \log 100$