0.35 log points to percentage

Question

What is 0.35 log points in percentages? I have no knowledge of this subject at all. From what I've gathered, it should be Percentage change = (e^log points - 1) * 100, so 42%. Is this correct?

Answer 1

The log points between $x$ and $y$ is the difference $$\log(x)-\log(y) = \log(x/y)$$

If $x$ differs from $y$ by a factor of $1+\frac{\%\Delta}{100}$ then we have $\frac{x}{y}=1+\frac{\%\Delta}{100}$,

$$\log(x)-\log(y) = \log(x/y) = \log\left(1+\frac{\%\Delta}{100}\right) $$ By exponentiation we have $$\mathrm e^{\log(x)-\text{log}(y)}=\mathrm e^{\log\left(\frac{\%\Delta}{100}+1\right)}=\frac{\%\Delta}{100}+1$$ that is $$ \%\Delta=\left(\mathrm e^{\overbrace{{\log(x)-\text{log}(y)}}^{\text{log points}}}-1\right)\cdot 100 $$