Sure, let's match each logarithmic equation to its corresponding [tex]$x$[/tex]-value step by step.
1. [tex]\(\log_4 (x) = 2\)[/tex]:
- The base is 4, and the logarithm value is 2.
- This means [tex]\(4^2 = x\)[/tex].
- Therefore, [tex]\(x = 16\)[/tex].
2. [tex]\(\log_3 (x) = 1\)[/tex]:
- The base is 3, and the logarithm value is 1.
- This means [tex]\(3^1 = x\)[/tex].
- Therefore, [tex]\(x = 3\)[/tex].
3. [tex]\(\log_{10} (x) = 3\)[/tex]:
- The base is 10, and the logarithm value is 3.
- This means [tex]\(10^3 = x\)[/tex].
- Therefore, [tex]\(x = 1000\)[/tex].
4. [tex]\(\log_5 (x) = 4\)[/tex]:
- The base is 5, and the logarithm value is 4.
- This means [tex]\(5^4 = x\)[/tex].
- Therefore, [tex]\(x = 625\)[/tex].
5. [tex]\(\log_2 (x) = 5\)[/tex]:
- The base is 2, and the logarithm value is 5.
- This means [tex]\(2^5 = x\)[/tex].
- Therefore, [tex]\(x = 32\)[/tex].
Now let's form the correct pairs:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
16 & \log_4 x = 2 & \log_3 x = 1 & 625 & \log_{10} x = 3 \\
\hline
\log_5 x = 4 & 1000 & \log_2 x = 5 & 32 & \\
\hline
\end{array}
\][/tex]
Pairs:
- [tex]\(\log_4 x = 2 \rightarrow x = 16\)[/tex]
- [tex]\(\log_3 x = 1 \rightarrow x = 3\)[/tex]
- [tex]\(\log_{10} x = 3 \rightarrow x = 1000\)[/tex]
- [tex]\(\log_5 x = 4 \rightarrow x = 625\)[/tex]
- [tex]\(\log_2 x = 5 \rightarrow x = 32\)[/tex]
Therefore, the pairs are:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\log_4 x = 2 & 16 \\
\log_3 x = 1 & 3 \\
\log_{10} x = 3 & 1000 \\
\log_5 x = 4 & 625 \\
\log_2 x = 5 & 32 \\
\hline
\end{array}
\][/tex]
