Questions: logp V = -y The equivalent equation is □

Transcript text: \[ \log _{p} V=-y \] The equivalent equation is $\square$

Solution

Solution Steps

To convert a logarithmic equation to its equivalent exponential form, we use the property that if $\log_b a = c$, then the equivalent exponential form is $b^c = a$. Applying this property to the given equation $\log_p V = -y$, we can rewrite it in exponential form.

Step 1: Understand the Logarithmic Equation

The given logarithmic equation is:

\[ \log_{p} V = -y \]

This equation states that the logarithm of $ V $ with base $ p $ is equal to $-y$.

Step 2: Convert to Exponential Form

To convert a logarithmic equation to its equivalent exponential form, we use the definition of a logarithm:

\[ \log_{b} a = c \quad \text{is equivalent to} \quad b^c = a \]

Applying this definition to the given equation $\log_{p} V = -y$, we get:

\[ p^{-y} = V \]