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Answer :
To convert the equation [tex]\(313,002.0188 = 2^x\)[/tex] to logarithmic form, you want to solve for [tex]\(x\)[/tex] using logarithms.
1. Understand that [tex]\(2^x = 313,002.0188\)[/tex] means you need to find what power [tex]\(x\)[/tex] you raise 2 to get 313,002.0188.
2. The logarithmic form of this equation is [tex]\(x = \log_2(313,002.0188)\)[/tex].
3. To find [tex]\(x\)[/tex], you can use a scientific calculator to compute the logarithm with base 2. Generally, calculators have a button for the logarithm in base 10 (log or common log) or base [tex]\(e\)[/tex] (ln or natural log), but you can convert these using the change of base formula:
[tex]\[
\log_2(313,002.0188) = \frac{\log_{10}(313,002.0188)}{\log_{10}(2)}
\][/tex]
or
[tex]\[
\log_2(313,002.0188) = \frac{\ln(313,002.0188)}{\ln(2)}
\][/tex]
4. When you carry out this calculation, you find that:
[tex]\[
x \approx 18.25581243671725
\][/tex]
So, the logarithmic form of the equation [tex]\(313,002.0188 = 2^x\)[/tex] is [tex]\(x \approx 18.25581243671725\)[/tex]. This means you raise 2 to approximately 18.256 to get 313,002.0188.
1. Understand that [tex]\(2^x = 313,002.0188\)[/tex] means you need to find what power [tex]\(x\)[/tex] you raise 2 to get 313,002.0188.
2. The logarithmic form of this equation is [tex]\(x = \log_2(313,002.0188)\)[/tex].
3. To find [tex]\(x\)[/tex], you can use a scientific calculator to compute the logarithm with base 2. Generally, calculators have a button for the logarithm in base 10 (log or common log) or base [tex]\(e\)[/tex] (ln or natural log), but you can convert these using the change of base formula:
[tex]\[
\log_2(313,002.0188) = \frac{\log_{10}(313,002.0188)}{\log_{10}(2)}
\][/tex]
or
[tex]\[
\log_2(313,002.0188) = \frac{\ln(313,002.0188)}{\ln(2)}
\][/tex]
4. When you carry out this calculation, you find that:
[tex]\[
x \approx 18.25581243671725
\][/tex]
So, the logarithmic form of the equation [tex]\(313,002.0188 = 2^x\)[/tex] is [tex]\(x \approx 18.25581243671725\)[/tex]. This means you raise 2 to approximately 18.256 to get 313,002.0188.
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