Sure, let's pair each logarithmic equation to its corresponding [tex]\( x \)[/tex]-value step by step.
1. For the equation [tex]\(\log_2 x = 5\)[/tex]:
- The corresponding [tex]\( x \)[/tex]-value is [tex]\( 32 \)[/tex].
2. For the equation [tex]\(\log_4 x = 2\)[/tex]:
- The corresponding [tex]\( x \)[/tex]-value is [tex]\( 16 \)[/tex].
3. For the equation [tex]\(\log_5 x = 4\)[/tex]:
- The corresponding [tex]\( x \)[/tex]-value is [tex]\( 625 \)[/tex].
4. For the equation [tex]\(\log_{10} x = 3\)[/tex]:
- The corresponding [tex]\( x \)[/tex]-value is [tex]\( 1000 \)[/tex].
5. For the equation [tex]\(\log_3 x = 1\)[/tex]:
- The corresponding [tex]\( x \)[/tex]-value is [tex]\( 3 \)[/tex].
Using these pairs, we can fill in the boxes:
- [tex]\( 32 \square \log_2 x = 5 \)[/tex]
- [tex]\( 16 \square \log_4 x = 2 \)[/tex]
- [tex]\( 1000 \square \log_{10} x = 3 \)[/tex]
- [tex]\( 625 \square \log_5 x = 4 \)[/tex]
- [tex]\( 3 \square \log_3 x = 1 \)[/tex]
Thus, the correct pairs are:
[tex]\[
32 \quad \log_2 x = 5 \\
16 \quad \log_4 x = 2 \\
1000 \quad \log_{10} x = 3 \\
625 \quad \log_5 x = 4 \\
3 \quad \log_3 x = 1 \\
\][/tex]
