Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Match each logarithmic equation to its corresponding [tex]$x$[/tex]-value.

\begin{tabular}{|c|c|c|c|c|}
\hline 16 & [tex]$\log _4 x=2$[/tex] & [tex]$\log _3 x=1$[/tex] & 625 & [tex]$\log _{10} x=3$[/tex] \\
\hline [tex]$\log _5 x=4$[/tex] & 1,000 & [tex]$\log _2 x=5$[/tex] & 32 & \\
\hline
\end{tabular}

[tex]$\square$[/tex] [tex]$\square$[/tex] [tex]$\square$[/tex] [tex]$\square$[/tex]



Answer :

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]