Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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]

Sagot :

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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.