Question
Write the following exponential equation in logarithmic form. Assume all variables are positive and not equal to one. \( 2^{c}=a \)
Ask by Johnson Brooks. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( c = \log_2 a \)
Solution
1. Start with the given exponential equation:
\[
2^c = a
\]
2. Recall the definition of a logarithm: if \(\displaystyle b^x = y\), then
\[
x = \log_b y.
\]
3. Applying this definition to our equation, we have:
\[
c = \log_2 a.
\]
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Simplify this solution Extra Insights
To convert the exponential equation \( 2^{c} = a \) into logarithmic form, you would express it as \( \log_{2}(a) = c \). This means that the logarithm base 2 of \( a \) equals \( c \), showing the power to which 2 must be raised to get \( a \). Understanding logarithms can also give you insight into compound interest, population growth, or even the pH scale in chemistry! For instance, if you’re calculating interest on savings, knowing how to manipulate exponential and logarithmic equations can help you determine how long it’ll take to double your investment. So, get comfy with those log formulas!
