1, and both sides are multiplied by X.

2. Both sides take the power of e at the same time (that is, the power of e). Note that ln is gone, because ln is a logarithm based on E, and the powers of ln and E are inverse operations.

Logarithmic application

Logarithm has many applications both inside and outside mathematics. Some of these events are related to the concept of scale invariance. For example, each chamber of the Nautilus shell is a rough copy of the next chamber, scaled by a constant factor. This leads to a logarithmic spiral. Benford's law about the distribution of pre-derivatives can also be explained by scale invariance.

Logarithm is also related to self-similarity. For example, the logarithmic algorithm appears in the algorithm analysis, and the algorithm is decomposed into two similar smaller problems, and their solutions are patched, and the problem is solved. The size of self-similar geometric shapes, that is, shapes whose parts are similar to the whole image, is also based on logarithm.