Writing an exponential formula where the factor decreases by $10%$ each time

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I am attempting to write a formula for the following:

if Input $0 - 50$ Result is $1$,

if Input $51 - 120$ Result is $2$,

if Input $121 - 271$ Result is $3$,

if Input $271 - 579$ Result is $4$,

if Input $580 - 1169$ Result is $5$,

and so on...

The maximum allowed value from result $1$ to result $2$ is a multiplication of $2.4$ times, but multiplying factor of this number I would like to decrease by $10 percent$ each time, so result $2$ to result $3$ is $2.26$ (1 + 1.4 * 0.9), result $3$ to result $4$ is $2.134$, result $4$ to result $5$ is $2.0206$ and so on.

i have rounded all inputs to the nearest significant figure as all inputs will be in whole numbers

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-Edit- This answer was written before the change to the problem including this "10% decrease in the increase amount each time" occurred.

$$\left\lceil\log_{2.4}\left(\frac{x}{50}\right)\right\rceil + 1$$

with the following exception made for when $x<50$ that it should output $1$