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.

Solution 1:

Hint

This should help:

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

Solution 2:

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 ......