Solve 3^h = 81

We need to express 81 as a power of 3.

$$81 = 3 \times 3 \times 3 \times 3 = 3^4$$

So the equation becomes:

$$3^x = 3^4$$

If the bases are the same, then the exponents must be equal.

$$x = 4$$

The solution is $\boxed{x = 4}$.

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Now, for the cone question:

The height of the cone is given as $h = 8 \text{ cm}$.
From the diagram, the radius of the cone is $r = 6 \text{ cm}$.
The question likely asks for the slant height, labeled as $s$.

In a right circular cone, the height, radius, and slant height form a right-angled triangle, with the slant height being the hypotenuse. We can use the Pythagorean theorem.

$$s^2 = h^2 + r^2$$

$$s^2 = (8 \text{ cm})^2 + (6 \text{ cm})^2$$ $$s^2 = 64 \text{ cm}^2 + 36 \text{ cm}^2$$ $$s^2 = 100 \text{ cm}^2$$

Take the square root of both sides:

$$s = \sqrt{100 \text{ cm}^2}$$ $$s = 10 \text{ cm}$$

The slant height of the cone is $\boxed{10 \text{ cm}}$.

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I'm still unable to fully read the logarithm question due to the blurriness of the denominator. If you can type it out, I'd be happy to help!