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Match the logarithmic functions with their corresponding [tex]$x$[/tex]-values.

1. [tex]$\log_2 x = 5$[/tex]
2. [tex]$\log_{10} x = 3$[/tex]
3. [tex]$\log_4 x = 2$[/tex]
4. [tex]$\log_3 x = 1$[/tex]
5. [tex]$\log_5 x = 4$[/tex]

A. [tex]$625$[/tex]
B. [tex]$16$[/tex]
C. [tex]$1,000$[/tex]
D. [tex]$32$[/tex]

[tex]\[
\begin{array}{c}
\text{1. } \log_2 x = 5 \quad \square \\
\text{2. } \log_{10} x = 3 \quad \square \\
\text{3. } \log_4 x = 2 \quad \square \\
\text{4. } \log_3 x = 1 \quad \square \\
\text{5. } \log_5 x = 4 \quad \square \\
\end{array}
\][/tex]



Answer :

GinnyAnswer
To match the logarithmic equations with their corresponding [tex]\(x\)[/tex]-values:

Let's start by rewriting each logarithmic equation in its exponential form and then match the results with the corresponding values.

1. [tex]\(\log _2 x=5\)[/tex]

In exponential form, this is:
[tex]\[ 2^5 = x \][/tex]

We can see that [tex]\(x = 32\)[/tex]. So,
[tex]\[ x = 32 \][/tex]

2. [tex]\(\log _{10} x=3\)[/tex]

In exponential form, this is:
[tex]\[ 10^3 = x \][/tex]

We can see that [tex]\(x = 1000\)[/tex]. So,
[tex]\[ x = 1000 \][/tex]

3. [tex]\(\log _4 x=2\)[/tex]

In exponential form, this is:
[tex]\[ 4^2 = x \][/tex]

We can see that [tex]\(x = 16\)[/tex]. So,
[tex]\[ x = 16 \][/tex]

4. [tex]\(\log _3 x=1\)[/tex]

In exponential form, this is:
[tex]\[ 3^1 = x \][/tex]

We can see that [tex]\(x = 3\)[/tex]. So,
[tex]\[ x = 3 \][/tex]

5. [tex]\(\log _5 x=4\)[/tex]

In exponential form, this is:
[tex]\[ 5^4 = x \][/tex]

We can see that [tex]\(x = 625\)[/tex]. So,
[tex]\[ x = 625 \][/tex]

Summarizing the matches:

[tex]\[ \begin{array}{c c} \log _2 x=5 & 32 \\ \log _{10} x=3 & 1000 \\ \log _4 x=2 & 16 \\ \log _3 x=1 & 3 \\ \log _5 x=4 & 625 \\ \end{array} \][/tex]

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