4) $$ { }^{5 x} $$, Both of these functions grow as $$ x $$ gets larger and larger. Which function eventually exceeds the other? $$ f(x)=8^{x-3} g(x)=10 x $$ Submit

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It seems that the equation $$ 8^x = 5120x $$ cannot be solved directly using the tools available. Instead, we can analyze the functions graphically or use a numerical approximation method.

### Step 6: Graphical Analysis

To determine where $$ f(x) $$ exceeds $$ g(x) $$, we can evaluate both functions at various values of $$ x $$:

- For small values of $$ x $$:
  - $$ x = 0 $$: 
    - $$ f(0) = 8^{-3} = \frac{1}{512} $$
    - $$ g(0) = 0 $$
  - $$ x = 1 $$:
    - $$ f(1) = 8^{-2} = \frac{1}{64} $$
    - $$ g(1) = 10 $$
  - $$ x = 2 $$:
    - $$ f(2) = 8^{-1} = \frac{1}{8} $$
    - $$ g(2) = 20 $$
  - $$ x = 3 $$:
    - $$ f(3) = 8^{0} = 1 $$
    - $$ g(3) = 30 $$
  - $$ x = 4 $$:
    - $$ f(4) = 8^{1} = 8 $$
    - $$ g(4) = 40 $$
  - $$ x = 5 $$:
    - $$ f(5) = 8^{2} = 64 $$
    - $$ g(5) = 50 $$
  - $$ x = 6 $$:
    - $$ f(6) = 8^{3} = 512 $$
    - $$ g(6) = 60 $$

### Step 7: Conclusion

From the evaluations, we can see that $$ f(x) $$ starts to grow significantly faster than $$ g(x) $$ as $$ x $$ increases.

To summarize, while $$ g(x) = 10x $$ is larger for small values of $$ x $$, $$ f(x) = 8^{x-3} $$ will eventually exceed $$ g(x) $$ as $$ x $$ becomes large enough.

Thus, the function $$ f(x) $$ will eventually exceed $$ g(x) $$.
$$ f(x) = 8^{x-3} $$ will eventually exceed $$ g(x) = 10x $$ as $$ x $$ becomes larger.

4) \( { }^{5 x} \), Both of these functions grow as \( x \) gets larger and larger. Which function eventually exceeds the other? \( f(x)=8^{x-3} g(x)=10 x \) Submit

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