The three rates you mention have very different meaning.

Inflation rate is the rate of change of a price index. As such, it can be negative and Daniel is right in pointing out that this may bring about to obvious problems when you try to take logs.

Interest rates can be negative too, as we recently experienced.

The exchange rate is a relative price (the price of a currency in terms of another currency): as such it cannot be negative and you can legitimately take logs of it.

Arun answer provides a constructive blueprint. The question you should ask yourself is: what do you want to measure?

If you are working on a single time series, taking logs of an inflation rate is impossible, taking logs of an interest rate is pointless (no exponential trend to linearize), taking logs of an exchange rate can make sense (it can stabilize the variance of the time series).

If you are working on a model, and wishes to measure the elasticity to any of these variables of a left-hand side in logs, then the situation is a bit more complicated.

Remember that in the equation:

log(y) = a + b x

where a and b are coefficients, b is the semielasticity of y to x. The elasticity is given by b times x. This implies that you do not necessarily need to take the log af a RHS variable if you want to estimate an elasticity. Semi-log model allows you to estimate (variable) elasticities. The estimated elasticities are variable because they are obtained as the product of a constant semi-elasticity times a variable... RHS variable! This implies tht you do not necessarily need to take the logs of a RHS variable if you wish to estimate an elasticity (provided the latter is not constant).

This is the solution usually adopted when estimating long-run money demand equations (e.g., Dreger at al., 2016).

The appropriate modelling choice depends as usual on the stochastic nature of the variables and on the underlying theoretical mode. Hope this helped.

Dreger, Christian, Dieter Gerdesmeier, and Barbara Roffia. "Re-vitalizing Money Demand in the Euro Area: Still Valid at the Zero Lower Bound." (2016).

https://blogs.sas.com/content/iml/2011/04/27/log-transformations-how-to-handle-negative-data-values.html

Another technical fix along the same line as Hamit's is you could use the inverse hyperbolic sine transformation. This transformation is similar to the log for positive values, but is defined for non-positive values, too.

Burbridge, John B., Lonnie Magee and A. Leslie Robb. 1988. "Alternative Transformations to Handle Extreme Values of the Dependent Variable". Journal of the American Statistical Association, 83(401): 123-127.

1. I agree that we can apply log to a ratio, but what about the case when the ratio is in decimal? Because taking the log of a decimal may change the nature of data; it will give us negative values. Will that not affect our estimates?.

2. Alberto and Daniel have pointed out the problem in taking log on inflation; it may have some negative values and the log is not defined for negative values. But coincidentally in my data there is no negative value for inflation rate. So taking a log will not create a problem. But does it still make sense to take log on such a variable which is already shown in percentage? Because in this case the coefficient of inflation will give us elasticity interpretation (percentage change of percentage). Can we proceed with such kind of coefficient?

look at the following link to change negative values to logarithm.

https://www.researchgate.net/publication/291408442

I think it is sufficiently okay to leave inflation rate without log whether having negative values in the data or not. Since inflation rate is already in percentage and can only be interpreted in percentage.