To solve the equation 4.150 - 3x = 3.10^2, we can start by subtracting 4.150 from both sides:

4.150 - 3x - 4.150 = 3.10^2 - 4.150

This simplifies to:

-3x = 310 - 4.150

Next, we can subtract 4.150 from 310:

-3x = 305.85

To isolate x, we divide both sides of the equation by -3:

x = 305.85 / -3

x ≈ -101.95

Now, let's solve the equation 2.3^x = 10.3^12 + 8.27^4.

We can start by subtracting 10.3^12 from both sides:

2.3^x - 10.3^12 = 8.27^4

Next, we can take the logarithm of both sides to solve for x:

log(2.3^x - 10.3^12) = log(8.27^4)

Using logarithm properties, we can bring down the exponent:

x * log(2.3) - log(10.3^12) = 4 * log(8.27)

Simplifying further:

x * log(2.3) - 12 * log(10.3) = 4 * log(8.27)

Now, we can substitute the values of the logarithms using a calculator:

x * 0.3617 - 12 * 1.0128 = 4 * 0.9163

0.3617x - 12.1536 = 3.6652

Next, we can add 12.1536 to both sides:

0.3617x = 3.6652 + 12.1536

0.3617x = 15.8188

Finally, we divide both sides by 0.3617 to solve for x:

x = 15.8188 / 0.3617

x ≈ 43.68