How can I get the effect associated with a $k$-unit increase in the predictor in logistic regression? The outcome of interest is disease yes/no (coded 1/0) and the continuous variable of interest is measured in nmol/L. The output of the regression suggests that a 1 unit change in the predictor (presumably a 1 nmol/L increase) results in a 3% reduction in disease. This is significant. However, I think it would be more meaningful to consider the reduction in disease for every 10 nmol/L increase in the continuous variable. Is this possible? 
Incidentally I did log transform to base 2 as per a previous suggestion and this showed that a doubling in the continuous variable resulted in a 35% reduction in disease outcome.
 A: Suppose you have a binary outcome $Y_i$ and a single predictor $X_i$ and fit a logistic regression model: 
$$ \log \left( \frac{ P(Y_i = 1 | X_i) }{ P(Y_i = 0 | X_i) } \right) = \beta_0 + \beta_1 X_i$$
Then, $e^{\beta_1}$ is the multiplicative change in odds that $Y_i=1$ associated with a 1-unit increase in the predictor. For example, $e^{\beta_1} = 1.03$ then a one unit increase in $X_i$ leads to $3\%$ increase in the odds that $Y_i = 1$. 
Now, if the natural scale of $X_i$ is not of interest to you, then you can re-scale so that $e^{\beta_1}$ is the percentage change of interest. For example, if you're truly interested in the effect of a $10$-unit change in $X_i$, as you appear to be here, then $e^{10\beta_1}$ is the quantity of interest. In general, $e^{c \cdot \beta_1}$ is the change in odds associated with a $c$ unit increase in the predictor. 
You can also, equivalently, scale your predictor variable before the analysis to get the same result. That is, if you instead used the predictor $X^{\star}_i = c \cdot X_i$ then the resulting regression coefficient would be interpreted as the effect for a $c$ unit increase in the original predictor, $X_i$. 
