What is log_{10}(A*e^{-q/r}) ?

The solution to log_{10}(A*e^{-q/r}) is log_{10}(A)-(log_{10}(e)q)/r

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simplify log_{10}(A*e^{-q/r})

simplify

lo g_{10} (A \cdot e^{- \frac{q}{r}})

lo g_{10} (A) - \frac{lo g _{10} ( e ) q}{r}

Solution steps

lo g_{10} (A e^{- \frac{q}{r}})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (A e^{- \frac{q}{r}}) = lo g_{10} (A) + lo g_{10} (e^{- \frac{q}{r}})

= lo g_{10} (A) + lo g_{10} (e^{- \frac{q}{r}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (e^{- \frac{q}{r}}) = - \frac{q}{r} lo g_{10} (e)

= lo g_{10} (A) - \frac{q}{r} lo g_{10} (e)

Multiply

\frac{q}{r} lo g_{10} (e) : \frac{lo g _{10} ( e ) q}{r}

= lo g_{10} (A) - \frac{lo g _{10} ( e ) q}{r}

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What is log_{10}(A*e^{-q/r}) ?
The solution to log_{10}(A*e^{-q/r}) is log_{10}(A)-(log_{10}(e)q)/r