Questions: Write the equation in exponential form. Assume that all constants are positive and not equal to 1. logu(p) = q

Write the equation in exponential form. Assume that all constants are positive and not equal to 1.

logu(p) = q
Transcript text: Write the equation in exponential form. Assume that all constants are positive and not equal to 1. \[ \log _{u}(p)=q \]
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Solution

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Solution Steps

Step 1: Convert Logarithmic Equation to Exponential Form

Given the logarithmic equation:

\[ \log_{u}(p) = q \]

we can convert it to its exponential form using the definition of a logarithm. This gives us:

\[ u^q = p \]

Step 2: Substitute Values

Assuming \( u = 2 \) and \( q = 3 \), we substitute these values into the exponential equation:

\[ 2^3 = p \]

Step 3: Calculate \( p \)

Now, we calculate \( p \):

\[ p = 2^3 = 8 \]

Final Answer

The exponential form of the equation is:

\[ \boxed{2^3 = 8} \]

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