Question

Math

Posted 4 months ago

```
Write the equation in logarithmic form.
Assume that all constants are positive and not equal to 1 .
$5^{n}=a$
HintStarting with the graph of $f(x)=9^{x}$, write the equation of the graph that results when:
(a) $f(x)$ is shifted 5 units downward. $y=$
(b) $f(x)$ is shifted 2 units to the left. $y=$
(c) $f(x)$ is reflected about the $x$-axis. $y=$
```

Sign in to unlock the answer

Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Start with the given equation: $5^n = a$

step 2

Apply the definition of logarithms: $\log_b(a) = c$ if and only if $b^c = a$

step 3

Using the definition, rewrite $5^n = a$ in logarithmic form: $\log_5(a) = n$

Answer

$\log_5(a) = n$

Key Concept

Logarithmic Form

Explanation

The logarithmic form of an equation $b^c = a$ is $\log_b(a) = c$.

```
Question 2: Write the equation of the graph that results when $f(x) = 9^x$ is shifted 5 units downward.
```

step 1

Start with the function $f(x) = 9^x$

step 2

To shift the graph 5 units downward, subtract 5 from the function: $y = 9^x - 5$

Answer

$y = 9^x - 5$

Key Concept

Vertical Shift

Explanation

Shifting a graph downward by $k$ units involves subtracting $k$ from the function.

```
Question 3: Write the equation of the graph that results when $f(x) = 9^x$ is shifted 2 units to the left.
```

step 1

Start with the function $f(x) = 9^x$

step 2

To shift the graph 2 units to the left, replace $x$ with $x + 2$: $y = 9^{x + 2}$

Answer

$y = 9^{x + 2}$

Key Concept

Horizontal Shift

Explanation

Shifting a graph to the left by $k$ units involves replacing $x$ with $x + k$ in the function.

```
Question 4: Write the equation of the graph that results when $f(x) = 9^x$ is reflected about the $x$-axis.
```

step 1

Start with the function $f(x) = 9^x$

step 2

To reflect the graph about the $x$-axis, multiply the function by $-1$: $y = -9^x$

Answer

$y = -9^x$

Key Concept

Reflection about the $x$-Axis

Explanation

Reflecting a graph about the $x$-axis involves multiplying the function by $-1$.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question