$$ f(x)=\log _{2}(x+3) $$ and $$ g(x)=\log _{2}(3 x+1) $$. (a) Solve $$ f(x)=4 $$. What point is on the graph of $$ f $$ ? (b) Solve $$ g(x)=4 $$. What point is on the graph of $$ g $$ ? (c) Solve $$ f(x)=g(x) $$. Do the graphs of $$ f $$ and $$ g $$ intersect? If so, where? (d) Solve $$ (f+g)(x)=7 $$. (e) Solve $$ (f-g)(x)=5 $$.

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UpStudy AI · Accepted Answer

### Problem (a)

**Given:**
$$ f(x) = \log_2(x + 3) $$

**Task:**
Solve $$ f(x) = 4 $$ and identify the corresponding point on the graph of $$ f $$.

**Solution:**

1. **Set the equation:**
   $$
   \log_2(x + 3) = 4
   $$

2. **Convert the logarithmic equation to its exponential form:**
   $$
   x + 3 = 2^4
   $$
   $$
   x + 3 = 16
   $$

3. **Solve for $$ x $$:**
   $$
   x = 16 - 3 = 13
   $$

4. **Identify the point on the graph:**
   Since $$ f(13) = 4 $$, the point is $$ (13, 4) $$.

**Answer:**
Problem a Answer

To solve $$ f(x) = 4 $$:

$$
\log_2(x + 3) = 4 \implies x + 3 = 2^4 = 16 \implies x = 13
$$

A point on the graph of $$ f $$ is $$ (13,\ 4) $$.
**Problem (a) Solution:** Solve $$ f(x) = 4 $$: $$ \log_2(x + 3) = 4 \implies x + 3 = 16 \implies x = 13 $$ Point on the graph of $$ f $$: $$ (13, 4) $$.

and .
(a) Solve . What point is on the graph of ?
(b) Solve . What point is on the graph of ?
© Solve . Do the graphs of and intersect? If so, where?
(d) Solve .
(e) Solve .

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and . (a) Solve . What point is on the graph of ? (b) Solve . What point is on the graph of ? © Solve . Do the graphs of and intersect? If so, where? (d) Solve . (e) Solve .