# Comparing large exponents

Without calculator, I have to determine which of the following is larger:

$2^{350}$ or $5^{150}$

I know only very basic exponential laws, and haven't covered logarithms yet. Tried various algebraic simplification methods but had no luck.

Any help is much appreciated, thanks in advance.

Hint

This should help:

$$2^7=128>125=5^3$$

To evaluate these values, they must be placed on the same “platform”.

Find $$x$$ such that $$2^{350} = (x)^{50}$$. Similarly, find $$y$$ such that $$5^{150} = (y)^{50}$$.

These two numbers are now raised to the same platform and therefore can be compared (now).

If $$x > y$$ then..., otherwise ......