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Match each logarithmic equation to its corresponding [tex]\( x \)[/tex]-value.

[tex]\[
\begin{aligned}
&\log _2 x = 5 \quad \square \quad 32 \\
&\log _4 x = 2 \quad \square \quad 16 \\
&\log _5 x = 4 \quad \square \quad 625 \\
&\log _{10} x = 3 \quad \square \quad 1,000 \\
&\log _3 x = 1 \quad \square \quad 3 \\
\end{aligned}
\][/tex]

Sagot :

GinnyAnsweridn
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]